Vader finds Luke early and raises him, but is smarter enough to be super anxious about Palpatine. He knows his Master won't tolerate a powerful force sensitive like Luke running around as a free agent once he's old enough to be a threat, and he also knows exactly how horrible it is to serve Palpatine. He's able to put off deciding about this for a while--either because he manages to hide Luke from Palpatine, or because Palpatine doesn't push the issue while Luke is still a kid--and he gets at least a few years of raising Luke on his own, as Darth Vader, and while he's probably not really a good parent he does love his kid and is not cruel or violent, and they bond and have a good relationship. But then either Palpatine finds out or decides their time is up, and Vader knows he isn't powerful enough to protect Luke on his own.

Finally he decides the only safe place for Luke is with the Rebel Alliance, so he defects.

Almost no one even knew Vader HAD a son, so people are pretty shocked by that, and by how normal and nice Luke is. They want to be tolerant and not hold his family against him, but it's hard when he's so openly, visibly CLOSE to his terrible monster-dad.

Bonus if Bail Organa is still alive and he becomes one of the first ones to warm up to him, because he sees how much Vader cares about Luke and figures if he loves his kid then he can't be all bad (and that is a huge, huge relief.)

Double bonus if Luke lost his hand in this verse because Palpatine cut it off and mailed it to Vader as a mafia-style threat.