By stating that people's private business shouldn't concern others, you are also imposing a moral system on others. Throughout most of the history, and to many people even now, morality extends beyond what's observable to outsiders. See e.g. what most of the religions have to say on issues such as homosexuality or eating certain foods.
I'm not saying I have the right answer to all of this either, I'm just pointing out that your "morally neutral" stance isn't as neutral as you'd like to think.
>By stating that people's private business shouldn't concern others, you are also imposing a moral system on others
Only in mental gymnastics. Staying out of other people's private lives is not a question of my own morality but also the law in most western democracies. I am free to do whatever I want as long as my freedom doesn't negatively affect anyone else. If you're not affected by what I'm doing in private, why are you trying to involve yourself in it and act as a judge?
You're literally telling other people to stop doing stuff that you don't want them doing, specifically the act of telling others what to do.
You're allowed to do that, and we're allowed to point out that this doesn't work in practice and that the failure in practice is itself why we're not surprised or even upset about the hypocrisy.
The laws themselves were written to tell people what to do. That's why they come with actual punishments if you break them, not merely arguements like on the internet. And some of those laws do actually ban various acts associated with prostitution, though the stated reasons for such laws are also often out of sync with the consequences given what is easiest to prosecute.
Any that takes Leviticus seriously will have issues with both food and male homosexuality, though I'd point out that not all denominations of Christianity do so about homosexuality and most Christians expressly reject the bits about food.
People can be weirdly selective about such things, which is why I've not seen any suggestion by current christians that sacrificing a bird and dipping another bird in it's blood and then then shaking the blood soaked bird on the patient is a valid cure for leprosy. (Chapter 14:1-7)
Just realised that the text in Leveticus if taken literally says women are not allowed to have straight sex, only gay sex:
"""You shall not lie with a male as with a woman; it is an abomination""" - Leviticus 18:22
That said, translations are more of an art than a science, that's why there are so many of them.
It might instead be interpreted as a statement against being bisexual like me, where either gay or straight is fine but doing both is what the writer (from the Watsonian perspective, god) doesn't like.
I'm not saying I have the right answer to all of this either, I'm just pointing out that your "morally neutral" stance isn't as neutral as you'd like to think.