If males and females work mostly the same way, then "trans" as a concept simply cannot exist, because you cannot have a "male brain" or a "female brain".

However if RedPill is true and males and females are biologically hard-wired, so badly that "male" and "female" can straight up be whole categories of personality, then how can one explain the existence of female-like men (on the most visceral reactions like not having the instinct to lead and compete, being nurturing like a mother etc) and male-like women (on the most visceral reactions like not having the instinct to be "choosy/selective" when it comes to sex) ?

You can say society, but society induces roleplay, not instincts. If you say that society induced whole instincts re-writing, then maybe those instincts weren't so "hard-wired" after all.

Therefore only one option remains and it's acknowledging trans people as actually having male/female brains.