Why did Vader passively accept being killed and replaced at Palpatine's command?

I think you've completely misinterpreted that scene. Vader is not just passively standing there and watching the Emperor torture Luke to death, and far from showing how evil Vader had become, the scene is actually the point at which Vader comes back to the light side.

Have another look at the scene (thanks to @Paulie_D for linking it). From the moment the Emperor begins torturing Luke, Vader finds himself torn between his loyalty to the Emperor, and his love for his son. He looks at the Emperor, then down at Luke. Then back at the Emperor, then down at Luke. He knows he has to choose between them, and he chooses Luke: he picks the Emperor up and throws him to his death, at the cost of his own life.

The 2011 Blu-Ray version makes it more explicit, dubbing over a small "No" as he watches Luke get tortured, and then a louder "NO!!" as he moves forward and seizes the Emperor. It's quite apparent that, at that moment at least, he does care about Luke.

It's also worth noting that Vader was never actually that loyal to the Emperor in the first place. As early as Episode 3, he was planning to overthrow him and rule with Padme (which of course, did not happen):

ANAKIN: The Chancellor is weak! I can overthrow him!

He tries it again after he learns that Luke is his son. His entire motivation for trying to turn Luke to the Dark Side is so that they can overthrow the Emperor and rule together:

DARTH VADER: Join me, and together we will rule the galaxy as father and son!

As for why Vader seems to simply accept his fate when the Emperor orders Luke to kill him, there are three reasons:

• The Sith operate under the "Rule of Two", which means there can only be two of them at any one time. This naturally leads to a lot of backstabbing. In Episode 3, the Emperor orders Anakin to kill his previous apprentice, Count Dooku, just as he ordered Luke to kill Vader. Vader probably realizes the irony of the situation (especially since, as I already noted, he was planning to betray the Emperor).
• He's incapacitated and has just lost his hand and his lightsaber. There's really not much he can do to stop Luke.
• He feels he is beyond redemption and that death is the only way out:

DARTH VADER: It's too late for me, son.

TL;DR: Vader did care about Luke, he wasn't just standing there and watching him get tortured to death, and while he served the Emperor, he wasn't as blindly subservient as you believe him to be.

While many statements are made during Star Wars that imply the Dark Side "takes hold" of people; it seems to be mostly figurative. It talks about human nature, rather than some mysterious supernatural mind control.

You call Vader Anakin, but Obi-Wan Kenobi specifically avoids calling him Anakin after he is known as Darth Vader. Not only does he always address him as Darth (in episode IV), but he also reveals this as he talks to Luke later on:

A young Jedi named Darth Vader, who was a pupil of mine until he turned to evil, helped the Empire hunt down and destroy the Jedi Knights. He betrayed and murdered your father. Now the Jedi are all but extinct. Vader was seduced by the dark side of the Force.

And later:

Your father was seduced by the dark side of the Force. He ceased to be Anakin Skywalker and became Darth Vader. When that happened, the good man who was your father was destroyed. So what I have told you was true... from a certain point of view.

To OWK, Darth Vader is not Anakin anymore. He is no longer the human that he once knew.
Darth Vader somewhat agrees with his, up until the part where the fights for the good side at the end. Until then, he has not shown any desire to be known as Anakin.

Anakin killed a room of young padawans. This is by far the most heinous of his crimes. The Dark Side, though voluntary, requires a person to shut out their emotions and compassion. Palpatine needed to mold Anakin in order for him to be open to the Dark Side and its consequences. Vader is very much trying to not be human like Anakin was.

Combining this all together, Vader had many reasons to not act out of line in the scene you reference. Many possibilities exist:

• Luke is his son. Even if Vader wants to live, he might prefer to give his life over his son's. This theory counts whether Vader wants Luke to turn to the Dark Side or not.
• Vader's past crimes made him accept his imminent demise, as he feels it was deserved. This is in line with him turning against Palpatine in the end. Maybe that turnaround started as wanting to be punished himself (seeking absolution), before he realized Palpatine was the bigger evil.
• Vader may simply have been expecting Palpatine to be bluffing. Strong Force users are capable of sensing someone's heart and intentions (mainly Yoda and Palpatine do this). Vader maybe senses Luke's intentions too, or maybe he relies on Palpatine's senses to know that Luke is harmless.
• It took a whole lot of emotional shutting out for Anakin to be able to kill the padawans and later become Darth Vader. Vader may at this point simply be so emotionless and cold that he has little regard for life, including his own.

I always felt that Vader was constantly plotting against Palpatine after a certain point in their relationship.

Consider the films: Vader reaches out to Luke in ESB to join forces with him. This could be (and I think largely has been) interpreted as the classic Sith mantra of betrayal of one another. But I believe Vader likely understood the presence of his son quite early, perhaps even before A New Hope. And knowing of the presence of another Skywalker reassured him that he could potentially defeat the Emperor one day.

In ROTJ, Vader ADMITS to sensing Luke aboard the imperial shuttle Han piloted to Endor, but he allowed it to pass rather than block their entry. It is at this vital point that Vader's intentions should become clear to the viewer.

He knew that Luke had foolishly joined the mission where the Death Star would annihilate another rebel planet, or in this case a moon, and decided to act. When he told the Emperor of his having sensed Luke, the Emperor responded that Vader's feelings may not be clear.

How did Vader sense Luke, but the Emperor failed to do so? I believe it's because Vader began to focus his energy on shielding Luke's force signature from Palpatine, allowing him to pass unchecked, but also to cause the Emperor to second-guess his own foresight.

The Emperor says Luke will show himself to Vader, and Vader will bring Luke to him.

Now, hear me out: this is EXACTLY WHAT VADER WANTED.

The rebels on the surface are given plenty of time to plot and strategize while Vader quietly picks up Luke and takes off with him. Vader didn't bother to slay the rebels? Hmm.

Luke & Vader return to the Death Star where Vader now knows he must allow Luke to channel the dark side far enough to help him kill Palpatine. Vader pushes Luke to the edge, and Luke eventually does channel the dark side in combat (the look and feeling Luke has while hacking away at Vader's arm) and defeats Vader.

Vader is injured, but not fatally. He wanted Luke to be the one to kill Palpatine so he knew he could turn him.

However, here is another very pivotal moment.

The sight of the force lightning running through Luke is enough to jar Vader into channeling the light, and he realizes that he values Luke's life more than the Emperor's & his own at this point.

Seeing that Luke will not beat the Emperor alone, and knowing that it will take a sacrifice now to achieve his long-term goal, Vader flings the Emperor down the shaft, ending him once and for all.

I think Luke later completely understands the actions of his father, which allows him to view him in a more positive light than most rebels and Jedi generally did.

Fan theory over and out.

I've decided to add my own. It contains references to some things pointed by others and a few more I haven't seen anyone pointing - specifically, the Windu event (which mirrors this scene, and I think this is the key), which paired with Dooku's I think gives a stronger feel of what was happening:

The reason were:

• Darkside philosophy - The rule of two
• Mind control by Sidious (and a bit of 'Vader is stupid') - which is why Vader believed the darkside philosophy, and I'll point down what I think Lucas intended to be the clues on how he got free from it.

1) Sidious tells Anakin to Kill Dooku.

He states then that

• He was too dangerous to be left alive
• It was natural for him to seek revenge - and mentioned Anakins mother and the Sand people

2) Windu decides to kill Sidious

stating:

• He is too dangerous to be left alive (correctly), for he has the whole system at hands and incredible powers of manipulation. He said "I AM the senate" to Windu while "they (the Jedi)(...) don't trust democracy" to Anakin. And "I was right, the Jedi has taken over!" when he said before to Anakin the Jedi hand a plan to control the republic, that Anakin wasn't included in the plot, but soon he would be - which was exactly what he himself was about to do with Anakin at that very moment (and I think its possible that the fight with Luke, more than mirroring this one, could be also be 'planned' just add one more lock for Vaders submission, see Extra). Windu understood everything.

Sidious defends himselfs stating:

• (Pity face, Pity voice) "I am too weak, please don't kill me" (..then seconds later laughs and blasts Windu a mile a way)
• "I have the power to save the ones you love.. you must choose!"

3) Sidious killing Luke.

Luke:

• Is someone Vader loved - and protecting people he loved was Sidious main offer in order to get him to the Dark Side.
• Is not dangerous, definitely. He could be left alive. He was just a rebel against an empire and he even threw his light saber away in refusal of more violence. Differently from Dooku, and from Sidious himself against Windu..
• Luke says "Father, please!" (as Sidious pleaded against Windu, as Windu desperately tells Anakin not to believe him - but this time, clearly, the previous points, used by Sidious as lies to defend himself, apply truly here, showing how Sidious power can make him believe obviously absurd things - this one was absurd enough to make him recover consciousness. His faith on the darkside ends here)

Sidious fooled Vader into believing he killed Padme, the other person he loved and wanted to protect with his help. The "No!" Vader said when he killed Sidious, to protect the son he loved, was pretty exactly the same 'No!' he said when he 'learnt' he killed Padme (and 'No' he said when he cut Windus hand). Protecting people he loved was the lie Sidious used to get him into the darkside.

In the scene Sidious tells him he killed Padme, Vader states this must be absurd because he felt ('Force' feeling probably, a certainty given Vaders level of power) she was alive when they were together, but ended up believing in Sidious. And, this time, Sidious is killing his son. Vader learns Sidious has been fooling him the whole time. And as Sidious said seeking revenge for the death of a loved one (Vaders mother) was natural, Vaders act of killing him (for Padme, his mother(see Extra) and Luke) would also be 'correct' even according to his own teachings to Vader - so I think there was no way Vader wouldn't kill Sidious if he managed to put the pieces together (he had both 'light side' and 'dark side' philosophy against him).

In the final sequence, while Vader alternately looks at Sidious and Luke, and sees clearly what was happening, what happened with Padme and what has been happening to him, Sidious is talking to Luke:

"Fool.. Only now, at the end, do you understand? Your feeble skills are no match for the power of the dark side...you have paid the price for your lack of vision.."

Which is almost as a short and precise description of Vader's epiphany as one could make.

'Extra': There must be a few extra very important insights Vader gained at that time. At the time (at the opera) Sidious told Vader about Plagueis ability to a) Create Life b) Keep people from dying, and c) He taugh everything he knew to his apprentice (Sidious himself - and later he claims directly only one knew this secret but if he and Anakin worked together they could find out). b) Was told in response for Anakin stating that Jedi are selfless, only care for others and use their powers for good - Saving people he loves is caring about others - and Sidious had just said 'good was a point of view', so that was something for Anakin to think about. It was believed by the Jedi that Anakin was conceived by the midi chlorians - Sidious himself said that only the darkside was the path to such unnatural abilities and that by a) and c) he knew how to do it. It was apparently confirmed that Sidious actually created Anakin (https://screenrant.com/star-wars-anakin-father-emperor/2/). Not only that's absolutely huge but probably indicates that Annakins mother's death was also probably part of Sidious plan to seduce him. So Sidious plan could be far more intricate and evil - Created someone only to kill everyone he loved (while gaining his loyalty with the promise to do exactly the opposite), made he think everything was his fault, manipulated him through guilt, transforming him from a happy, loving, poor child raised by his mother into a mutilated, mind-controlled, half-droid murderer slave in the process. Maybe even Luke was part of the plan - why would inSidious baptize him Darth Vader('Dark Father')? In the opera, Sidious said Plagueis became so powerful the only thing he was afraid of was losing his power - he taught everything he knew to him and then he killed him in his sleep.. "Ironic..he could save others from death, but not himself" (with a subtle smile of satisfaction - maybe Plagueis taught him everything in order exactly to have some protection from someone else at the only time he was vulnerable - his sleep). Would this man ever allow slightest chance of an apprentice overpower, defeat or kill? The only thing he cared about was Power and the only thing he was afraid of was losing it - he never intended to let Vader have remotely enough knowledge/power to challenge him (let alone learn the deep secrets promissed to him as an offer to become a sith - which Sidious knew, but pretended he didn't), he only wanted to help him with his plot and keep him as slave general/bodyguard forever (when Anakin said the Sith 'think inwards, only about themselves', Sidious agreed - in the same conversation they spoke about 'being afraid of losing their power' and 'protecting the ones who love' - I think its reasonable consider that Sidious only loves himself). That all would make him the most evil and cunning villain I've ever heard of. Hannibal is a pussy next to this.

All of the answers above are top-notch, but another, more literal reason exists. The Dark Side's natural philosophy that Vader abided by is what made him allow Sidious to convince Luke to kill him, and it's what made him stand at Sidious' side as he electrocuted Luke. Vader's submission to Sidious caused him to see his fight against Luke as a test to prove his strength to Sidious. Luke pretty much also saw it the same way even though he was their enemy.

Palpatine was extremely powerful, Darth Plagueis was well aware how powerful he was and still underestimated him. Palpatine hid his true power, and was able to manipulate Plagueis for a very long time. Palpatine starting manipulating Vader at a very young age.