You're full of enough hot takes to melt steel. Phobia means extreme aversion or fear. Your assertion that something does not exist does not mean it does not exist.
"Irrationally and disproportionately" doing a LOT of work there.
If you don't care to actively support trans people, "polite indifference" is the only other appropriate response, as they're not hurting anybody by simply existing - mind your own business and let them mind theirs.
As bad as this take is, I actually do think transphobic is too light of a term for these assholes. Transphobic can imply to some people that its not their fault for being disgusting in some way. We don't call racist nazis 'racephobic', 'blackphobic', or 'jewphobic'. We need a harsher term to label them is what I'm getting at. I will just refer to them as bigots for now.
There are all these Christian fundamentalists who have been told all their lives they'll go to hell if they're not one hundred percent completely straight all the time, and God sees them and knows what they're thinking. Assuming there's a biological element to homosexuality, a large portion of these people are not completely straight from nature's side. Assuming people are often excited by taboos, they might secretly be more bi-curious (or whatever the word is) than the average population.
For these people, every single step towards gay and trans rights is making it a little bit harder to live in complete denial. They cannot simply ignore it, because they're obsessed with it. One improper thought and they'll burn in hell.
Of course this crowd is terrified of trans people.