I think you're assuming a lot about what the interaction actually was about, how it happened, and why. And you're assuming that I don't know what being part of a marginalized group that gets constant shit thrown at feels like.

An apology is not in order when the person is making a big deal out of nothing, making shit up, and reframing what's being said to defend imaginary people or abstract ideas. Then add to that malice when things don't go their way. If I had said something about a particular person or something egregious, I would understand, but I said it about a drawing.

I have difficulty backing down in lots of scenarios but accidentally upsetting someone I didn’t mean to isn’t one of them.

You say that because you haven't met the whiteknights in the community who get upset on behalf of others or lose their shit when others don't follow their mental models of gender expression/identity. You know how white people will sometimes cry culture appropriation, and the natives are like, "uh, we're actually ok with that"? Yeah, they exist in the gay world too, and some are vicious and vindictive to the point of being abusive themselves. To me, it sounds like you're defending a Karen.