Why did they still accept Deckard into the family even after what he'd done in previous movies?

According to the screenwriter for the movies, Chris Morgan, they expected this "face turn" for Shaw to generate a little controversy.

Link to article but relevant parts copied below:

ENTERTAINMENT WEEKLY: You joined the franchise writing the screenplay for Tokyo Drift, the movie that introduced Han. When we first met Deckard, he was killing Han. How did you guys decide to turn his character in this film?

CHRIS MORGAN: There are a couple of things I would say. We don’t know his full story yet, so there are things we’re going to learn that I think will be cool when it comes to light.

Beyond that, I would say, Deckard’s character is not that dissimilar from Dom, in certain ways. The reason Dom went to jail in the original film is he did some violence against someone who hurt his family. Deckard’s story is not too far away from that. The reason he comes after our guys in the last film is because he has a similar code, and he looks after family. So at least there are some markers in there for these two guys. That felt like you might be able to turn him, in a way that you could start understanding what his motivations were.

I’ve got to tell you, I love him in this movie. I love him and Dwayne. I love the way he relates to the team.

And

EW: When you guys initially brought him on in the last couple of movies, was there always some notion of flipping him from an antagonist to joining up with the team?

CM: Bringing Jason into the franchise, we always had an understanding. His character is a man with a code, and he believes in it, and he has a lot of similarities to Dom.

There are things, as developers, that we know about the character that you guys, the audience, do not know. We have the luxury of getting to that. I think people will be surprised and interested in it. This movie gets to a little bit more about who he is, and we learn a lot of new things about him.

I think the response will be that, because of what happened to Han, there is going to be a residual drama and tension. We’re going to lean into that. We haven’t forgotten about it. We’re going to investigate all of that. But also, you can see, in this film, a little more in [Deckard’s] core, as well. I know it’s a little unsettling, I know it’s a little different. Maybe the audience isn’t expecting it. I think it’s all, in the end, going to be a really exciting, fun, valuable experience. They’ll come to understand.

It sounds like the upcoming movie(s), presumably including the Hobbs and Shaw spinoff will go into more details around the character and provide more insight into the new "team" dynamic. Plus, saving Toretto's son definitely earned him a whole load of brownie points.