Trying to redefine "woman" and "man", "female" and "male", "homosexual" and "heterosexual" - and then reengineering society by decree based on these controversial redefinitions - is going to get opposition across the board.
I think this is why it's become such a hot "culture war" topic, because it undermines the deeply-held views of many, many more people than just religious conservatives.
Take gay marriage for instance - this was fought both for and against on the basis of it being a same-sex union. But from the perspective of gender identity believers, if, for example, someone female merely identifies as male, then marries a male (who also identifies as male), then this is a "gay marriage" too. Despite this actually being a heterosexual pairing.
On top of this, where these beliefs have been forced into law and policy, it has caused actual physical harms. Women being raped and impregnated by male prisoners who identified their way into the female prison estate is amongst the worst of these. But lawmakers in states that have enabled this will claim it's progressive policy, somehow. Even though it's regressing back to over a century ago when mixed-sex prisons where commonplace and incarcerated women were at constant risk of sexual violence and exploitation from the men they were locked up with.