Look at the laws red states are trying to pass - that you must use the restroom that matches the sex on your birth certificate. Now, think about how that works for trans men and trans women that look very, very much like the gender they claim. You'll have trans men - often with beards and all after hormone therapy - forced to use that restroom your daughter uses. You don't think that will freak her out? You'll have trans women - full makeup, implants and all - forced to use the mens room. That opens them up to a lot of potential violent encounters.
Those laws aren't great either, but it wasn't red states that opened the can of worms.
This wasn't an issue until politicians came along. It wasn't great for men or women doing a poor job of trying to pass, but it was probably as balanced of a solution as is available and pretty much nobody spent time worrying or talking about where transgender people went to the bathroom.
But progressives in cities like Charlotte couldn't leave well enough alone, and let people work things out civilly. So now bathrooms bills have moved to the forefront of the culture wars and the people hurt the most are transexuals as now instead of just having an uncomfortable situation, they actually must commit a minor violation of law in some states just to use the same bathrooms they were using without incident a year ago.