I want to know how you justify to yourself that LessWrong is anything but childish.

I don't.

I often have conversations here that interest me, which is all the justification I need for continuing to have conversations here. If I stopped finding them interesting, I would stop spending time here.

Perhaps those conversations are childish; if so, it follows that I am interested in childish conversations. Perhaps it follows that I myself am childish. That doesn't seem true to me, but presumably if it is my opinions on the matter aren't worth much.

All of that would certainly be a low-status admission, but denying it or pretending otherwise wouldn't change the fact if it's true. It seems more productive to pursue what interests me without worrying too much about how childish it is or isn't, let alone worrying about demonstrating to others that I or LW meet some maturity threshold.