Most people have never been taught how to get past visceral dislike, and the existence of trans people squicks a lot of people. We will never succeed in teaching dispassionate analysis to any significant number of people.
For most it really is the 'They're transing the kids' that snags them as although a lie it has a strong emotional element that just works. Like trans people in athletics it's also a handy way to hide existing bigotry.
The facts are important, science not so much, emotional connection is everything.
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The facts are important, science not so much, emotional connection is everything.