Yes they really do think all those things. That's what their social (online and IRL) bubble/filter shows them.
Just as a GC one, if we are not careful, overstates the degree to which "woman" is being replaced by "gender neutral" alternatives in biological contexts, or the degree to which toilets are becoming gender neutral.
I think GC women, being generally older and educated back in the day when seeking out a range of sources, hearing opposing views directly and concluding ones own position only after understanding all views and considering each on its own merits was considered a fundamental requirement for any position one held, are usually less susceptible to the filter bubble, but I do try to read many perspectives and I can see the mechanism operating on all sides.
It's not surprising a side that believes concepts that hurt the ego are too dangerous and damaging to engage with should be more susceptible to filter bubbles.
Plus of course the small problem that since reality itself is anti trans, or at least anti the "men and women have always been gender roles underneath, and sex doesn't really affect anything so let's all just ignore it" version of trans, ultimately everyone, and everything, is anti-trans, not because of hatred or bigotry or lack of vision but simply in the same way reality is also anti-flying-pig.