No, this is not about the religious right. That's tribal and simplistic thinking.
A law banning misgendering certainly would be problematic, and not just to theists. There is already a growing tendency in the west towards curtailing free speech. Restrict free speech to only officially sanctioned stances and what are you left with? Only what politicians and mainstream media will tell you, and they have been gaslighting us on myriad issues for decades (at least).
Re: making calling a transwoman a "man" a hate crime. "Misgendering" a transwoman who looks, sounds and vibes feminine is simply misleading. No, they are not men. They are not women either, but they are no longer men once they've been neutered and recombobulated. Terms ranging from "eunuch" to "woman" can meaningfully be applied in various situations, but calling such a person "a man" is just an ideological position, and is loose and careless use of language.
However, if a transperson looks, sounds and vibes as their original gender, then it is difficult for acquaintances to think of them as anything else. Once such people start moving into female spaces, they will attract legitimate claims that they are "men".
We humans do like our categories, don't we? For instance, a very white person with a black grandmother will often claim to be "black" to gain benefits. According to mainstream media, we have only black and white people, with no in between, despite the fact that the vast majority of black people in western socialites are partly from high melanin stock and partly from low melanin stock. MLK must be rolling in his grave.
As for gender, it's mechanistic and mindless to claim that intersexed people are "men" or "women" if they are very androgynous and don't identify as one way or another. However, there needs to be parsing in elite sport, as shown by the dominance of the intersexed Albanian boxer at the Paris Olympics. All professional sport organisations need do is ban people with a certain degree of intersexed physiology from women's sports, without mislabelling them as "men". Amateur sport's clubs and women's refuges can make their own policies for admitting or rejecting trans- or intersexed people.
Where the religious right does come in is their hypocrisy of focusing on DNA, taking the very scientism approach that they usually reject. Maybe they should also consider the science when it comes to first trimester abortions?
Same with gender. Physical intersex conditions are real - so the claim that there are only two genders is as simplistic as saying that islands consist of only land and sea, ignoring the existence of shorelines. The excluded middle especially seems to apply when middling phenomena are rare or relatively insignificant.
We also ignore middle states with consciousness. Its believed that one is either conscious or not, with no grey area, ignoring the brief transitional states between sleep and waking. Yes, such states are very brief and relatively insignificant, but they exist.
Same with those who are either intersexed or psychologically of mixed gender. This is super basic and should not be controversial. Even back in the 8Os, I learned in psychology class that there are four broad mental gender orientations - masculine, feminine, androgynous (lots of both) and undifferentiated (little of both). Is it any surprise that some of the more mentally feminine of males and masculine of females would develop an identity, a sense of self, based on their obvious difference? They know they are different, and they will have various ways of dealing with it.
It's easy to point to the transvestites posing as transsexuals on Tik Tok etc and say trans is all about fetish and delusion, but these "fake transsexuals" have emerged due to the blurring of lines by activists. Personally, I would call such a person "she" to their face in much the same way as I'd call Edna Everage or other drag queens "she". Blind Freddy can tell what a masculine transvestite is under the dress, and no one needs me to pretend I am the only person aware enough to notice that the emperor is wearing no clothes, so to speak.
Gosh, this was going to be a short reply
