The bathrooms aspect of this is a religious issue. It appears to be a GOP or "conservative" issue because that's where the religious block has lurked a long time. GOP and conservatives would be foolish to be bullied by a religious faction in the party, and Trump is right to be more flexible than narrow minded bigots.
It sounds alarming to make black/white arguments like it's all about letting perverts in with America's little girls.
Data and facts won't back that up.
And what parent is not standing outside a public restroom, watching, when their little girls go in? In fact, that's the only way to catch any pervert using public restrooms for anything according the bathroom law or not.
There are probably as many men who prey on boys as men who prey on girls. Get data on that, and legislate fairly/consistently.
Men who are transgendering to female are very likely to have heterosexual preferences, meaning, as the see themselves as female, they prefer males as sexual partners. Get the data on that. They are less likely, not more, to target women, let alone little girls. Get the data on that. Neither are they HIGH on the kind of testosterone likely to make men violent and dangerous. That's like banning marijuana and legalizing alcohol.
The trans community lives on a spectrum between "passing" and not passing.
At the very least the passing should get a pass.
It IS POSSIBLE to give legal passes to any trans who would like to apply for one...if this bathroom thing is really a data backed issue.
Take existing institutions for example a college. There can be a voting block that scans a trans' pic, bio, and maybe video, giving a thumbs up or down to a "pass". There can be ways to insure fairness. Doesn't have to be a beauty contest.
Can be done for every public bathroom in the US and every public bathroom can be marked designating it's participation in the program.
Few can argue with a democratic process.