I don't know to what extent pedophilia is innate or immutable, but the fact that it causes harm is what sets it apart from sexual orientation.

Our only disagreement here is that I think this is all that matters, from a legal/utilitarian/messaging perspective. In a liberal paradigm (and just to be super clear here since these terms are all muddied now, I mean liberal as opposed to authoritarian, not conservative) it doesn't matter whether something is a choice or not, or how scandalized people are by another person's choice. All that matters is whether actions cause direct material harm and infringe on another person's rights. I believe this renders forced conversion therapy a moot threat, too, because that is an infringement on your rights, for which you committed no previous infringement of your own.

I also don't want homosexuality to be misunderstood as a choice because people assign moral values to choices.

They still do, though. The far right wants us to suck it up and make more white babies for the ethnostate (unless you're not white, in which case they want you deported or genocided, but that's another topic). The religious people want us to either stay celibate or get married/have kids with an opposite sex partner anyway, because they see homosexuality like any other sinful temptation that can and should be resisted. In both cases, our innate attraction, our desires, are beside the point; the expectation is that we align our actions with the collective ideal.