[Everything] Understanding the line of succession

I read everywhere "Because of R+L=J then that makes Jon the rightful ruler of the seven kingdoms." No if R+L=J is true, then Jon Snow is still a bastard. "But he is the oldest male so he is next in line to receive Winterfell." No, Sansa is the only stark child, known by the public, to be alive. Jon is still a bastard, which means, no matter how much all of us want it, he has absolutely no right to rule Winterfell. A bastard is a bastard, no matter who his parents were.