That is certainly one of the answers on the table, but my question that you recited concerns society's behavior not the individuals.
So, let me rephrase the question with a broader context.
How should society react to a male who perhaps as the result of pre-natal abuse or just a quirk of nature, has had every reason during his thinking life to thoroughly believe he is a female?
With that I am supposing his sin, if any, is his concern and not that of society.
I noted above that I believe modern medicine can effectively address the condition. Further, if society is going to provide medical benefits that should be included.
“has had every reason during his thinking life to thoroughly believe he is a female”
We should respond the same way we would for someone who believes he is a unicorn. We should expect and even REQUIRE people conform to REALITY rather than insisting everyone else pretend their delusions are true.
As you know, this is a difficult question. How SHOULD society react? With compassion and firm boundaries. (addressed in other posts) How DOES society/human nature react? Pursuant to our own self-interest and fears, as usual.
It is difficult if not impossible to enact "love the sinner, hate the sin" when the sinner immediately rejects your efforts to reach out as soon as they realize you don't condone their sin. (For instance, I love my gay friends but utterly reject gay "marriage." For them, to reject gay marriage is the equivalent of rejecting them.)
This is a serious obstacle. Ideas on how to overcome it? I also think that the labeled person has to be open to possibility that someone might love them but reject their sin. How many LGBTQ+s do you know that are?
I do believe the fires of division have been stoked to quite a blaze in recent years.