Why was Athelstan the most important person in Ragnar's life?

While this question may go beyond the scope of SE, I'll try to answer to the best of my knowledge.
Disclaimer: I have only seen the first 3 seasons so far.

Ragnar is atypically interested in the Britons; especially compared to his fellow vikings who see the Britons as nothing but raidable targets. Ragnar, having been a farmer in a region with a horrible agriculture, understands the value of fertile soil.

Ragnar is a fierce warrior, but his intellect is his biggest asset. He's clever and outwits his enemy. If you're intending to be this clever, you need to have a curious mind, willing to learn and understand. The average viking doesn't care about the finer points of catholicism; but Ragnar knows that he can use this knowledge to his advantage.

Enter Athelstan.

He's a Briton monk (plus a scribe, so he knows his books) who is open minded enough to regard the vikings not as inferior heathens, but as people with a different culture. When Ragnar met Athelstan, he was immediately invested in him because of the knowledge Ath could provide him with.
Through Ath, Ragnar has learned much about Briton culture, he also learns to speak the language (which is a big bonus for diplomatic interactions) and sees the world in a different way.

Many vikings are shown to think lesser of Athelstan and the Britons. Conversely, many Britons (especially the religious ones) think of the Vikings as uncivilized barbarians. Both sides think that the other side is impossible to reason with.
But both Athelstan and Ragnar are not blinded by intolerance like so many of their brothers. They see the human side to other people, regardless of where they are from.

But this only provides the setup for why Ragnar was interested in Athelstan. Why was Athelstan interested in Ragnar? And more importantly, how did they manage to become friends (enough that Athelstan chooses to stay in Kattegat over going home, when Ragnar is the only one who really likes him).

I think Athelstan is a kindred spirit to Ragnar; they are both eager to learn of the other's culture. Athelstan is a scribe who has read many things (including most scientific knowledge that was available at the time), but he experienced little of it (because he spent his days copying books).
Ragnar is the opposite. He's a hands on guy, with street smarts; who lacks academic knowledge. But they are both passionate about learning new things, especially things that seem foreign to them.

Ragnar kept Athelstan by his side because he was useful (providing information and being their translator and ambassador when vising Britain). However, because both men are not only open to different cultures but actively interested in them, they spend a lot of time talking about differing ideas about life, culture and god(s). They are both able to respect other ideologies even if they don't believe in them.

A great example of this is the episode where they (vikings + Athelstan) go on a retreat to celebrate a festival (to prevent Ragnarok, iirc). Athelstan is interested in the festival and its activities, but is clearly perturbed by the last sacrifice: humans. You can see him struggling with it, because it is almost the definition of barbarian behavior (as he was taught by the Britons).
However, he moves past his own judgment and defers to that of the vikings. It's not his place to question their belief. The vikings were more than happy to explain and discuss it; but it would be wrong to make them change their ways because it makes Athelstan uneasy.

And from that, a true friendship grew. Athelstan and Ragnar personify the Norse/Briton alliance that could potentially form.
They show that it's possible, even if it's not likely on a large scale (due to intolerance from either side)

On a personal note, I really like Athelstan and Ragnar. Their friendship makes sense, their discussions are interesting, and they pull focus to how different cultures can still learn to respect eachother.

King Ecbert, on the other hand, is much more pragmatic in his approach. Ecbert sees the potential of allying with the Vikings (because he quarrels with the other Briton kings and could use a good army); and he cozies up to Athelstan because

• Athelstan understands Ecbert and his intentions better than Ragnar does, due to cultural differences.
• Athelstan does not benefit from any fighting between Ecbert and the vikings, so he can be trusted to not turn the vikings against Ecbert.
• Athelstan not only speaks for the vikings, but can also persuade them (for as long as Ragnar agrees or trusts it)

The simple answer is that Athelstan is an empath and Ragnar and Ecbert are drawn to him for all the reasons that empaths attract toxic people.