People are quite willing to overlook celebrities that boinked or dated young (often underage) girls. Although, dating a 16 year old is a bit different than a 6 year old, but my point being is that the general public is willing to "forget" about most anything as long as they like you and think you're a good guy.
No doubt there would be some people rail against Superman, and go on their "wake sheeple!" rants, but for the most part society would whistle and look the other way... After all, it's not like they could stop him if they wanted, and he literally protects 7 billion people from complete annihilation almost everyday... And it's not like he's raping them or anything. Maybe we should just let him have this?
See... It's scarily easy to justify. Sure it might shock people at first, and it'd be a huge news story when it came out, but Superman would publicly deny it, and a lot of people would support him. Sure, everyone would probably know the truth, but there's no proof. It's the word of a bunch of 8-year-olds against the Man of Steel. And they're probably sluts anyway.
Plus, as people would quickly lose interest in that whenever Lex announces his bid for presidency or whatever. People have short attention spans. And so Superman would continue to publicly protect the world while quietly getting some loli action on the side. Hell, you just know there would be a few parents who would even encourage it.
I think the real question is why he doesn't just molest them as Clark Kent. Or better yet, create a new persona (Ultraman?) to fuck kids. He can publicly play the hero while also playing the villain. Sure, Lex would probably see through it, but it would just come off as another one of his "I hate Superman" conspiracy style rants... Bruce would probably see through it too, but as >>79709225
mentions, he doesn't have a lot of room to talk.