I don't think so. I don't think the others would like it, but they're still family and they would accept it.

Edward left to rebel, then came back when he stopped.

Well, I wasn't asking if they would stop caring about anyone. I don't that's even a possibility, since their traits are compassion and love.
I just mean will they allow the one who chooses to kill humans to stay with them.

Yes... But having visitors and allowing vampires who kill people to live with them forever are two different things.

I'm still not asking if Carlisle and Esme are capable of caring for vampires who kill people. I already know they are. That's not the question.
You do know that they didn't invite any of the vampires in Breaking Dawn to live with them forever, right?

I agree with SarahCorine.Carlisle would not send him or her away if they were to drink human blood.He may not like it but Carlisle is a loving and compassionate man,but if any were to switch to drinking human blood they would still be a part of the family no matter what.

I don't think he would. He loves each member of his family and understands the struggle to abstain from animal blood. All of them do.
It's not in his nature to judge someone based upon what they feed on and considering that it's his family I think he'd respect that decision. As ebcullen4ever said, he might not like it but he would still accept them as a member of the family.

Yes, because if one of them was drinking human blood freely it'd make it that much harder for the rest to stick to an animal blood diet. Feeding on humans would also be an insult to Carlisle's beliefs and his respect for human life. I think he'd try to persuade that person to return to an animal blood diet, but if that didn't work he'd respect the individual's choice enough not to lock him or her up and force them to feed off animals only.

He'd only do so if a Cullen deliberately chose to feed on humans long term though. He'd live with someone who'd slipped up and fed on a human once or twice - that's happened in canon. And he'd take the family member back if he or she returned to animal blood - that's what happened with Edward.