If it's just a word and makes no difference then there should be no issue with using "he" to refer to any and all individuals of the male sex.
It's obviously much harder for you to use a different pronoun than for them to have their entire gender identity invalidated. Would you like for people to misgender you constantly and purposefully?
Your life must be so hard. I feel bad for you to have to use a different word to refer to someone. Maybe have some basic decency and respect for others?
Well then, consider that it really is not my problem if these males are offended by the simple word "he".
Have you heard of the Stroop effect?
More to the point, I've no interest whatsoever in encouraging a man's fantasy "woman" identity, quite the opposite in fact.
Perhaps these men would consider giving women and girls the basic decency and respect of refraining from such misogynistic appropriation.
They could even pick another word to describe themselves, given that "woman" is already taken. What's so hard about using a different word?