I have zero problems with people dressing however they like, having whatever affectations they want and having sex with whoever is willing. I might not always find it tasteful, but that cuts both ways I'm sure so we can agree to be civil. The buck stops when you try to shame me for not calling a man a woman. Using pronouns should be a kindness like holding the door open for a disabled person, not something that sends emotional children into a socially supported temper tantrum when absent.
The "men with gender identity issues" referred to by parent have this up-side-down, instead thinking that "social transitioning" aka "living as a woman" is a step towards being a woman, this is not destroying notions of gender, this is elevating gender over sex
That would be nice, but you have it backwards. In most cases the an attempt to make gender more central and essential, rather than less, by decoupling it from biology.
Which is why in some parts of the country children are sometimes being told that if they like boy sterotyped activities like tree climbing or boy stereotyped attire that you are a boy, rather than saying any activity or attire is available to anyone.
Rather than erasing gender it's power as a tool for enforced conformity is amplified by eliminating any requirement for agreement with a person's biological properties.
To exaggerate in order to make the point, it's as if we've gone from: "It's a womans' job to do the dishes" to "Anyone can do the dishes." to "The person doing the dishes is a woman, by definition."-- and the middle state's inclusiveness is increasingly seen as hateful because it denies people the ability to identify as a gender other than the one suggested by their biology through the performance of stereotyped behavior.
Erasure of "mothers" seems contrary to the trend at first blush, but it's made more clear when you see the suggested replacements like "birthing person" or "breeder"-- in this world view "mother" is a biological function, so it must be decoupled from gender so that the strongest possible gender sterotypes can be imposed on people regardless of their biological abilities.
For example, I don't think that anybody actually holds the sentence "The person doing the dishes is a woman, by definition" as true in their heads. That's simply not a thing people believe, anywhere along the political (or any other) spectrum.
If you actually talk to trans people, you'll find that most of them fall into the "nonconforming" bucket rather than some gender essentialist one. A lot of them are non-binary or otherwise have gender/sex identities that don't cleanly map onto maleness or femaleness. Given that state of affairs, it's a remarkable stretch to think that these people themselves would see neutral language as "hateful." And, in fact, they don't.