Well we can't exactly not care for private lives. For the certain GOP individuals who preach the moral high ground and then turn out to be hypocrites when they commit the same acts they condemn. Those people should certainly be reviled.
As for Weiner, yes I don't care much for his private life because it wasn't illegal and he doesn't really preach morality but I do care how he is dragging down the rest of the Democratic Party.
Yes I agree that for many situations, a person's private life shouldn't be considered. Thomas Jefferson, JFK, and Bill Clinton have all done less than admirable things in their private lives but were some of the greatest Presidents we've had.