I have little fear of this actually happening. To me, the real fear is that there exists a mindset of people who seem to think this sort of thing is OK. This would be the same thing as if some lawmaker were to propose reinstitution of legal slavery. It's the brain of this person (and his disciples) that's broken, and that he may be listened to and considered seriously is troubling.
But the actual imposition of this law doesn't seem to be likely. The last credible legislation banning trans folk from using the needed bathroom was in Maryland a few years ago, and it was defeated. Every other attempt in any other state since then has largely been political posturing without the necessary support needed to make it fly. It's a sad attempt by said legislators to get some press coverage so they can look good in front of their redneck constituents.
And if they fail in their holy mission - great! They're political martyrs, and they can blame the defeat on the alleged overwhelming liberal bias that is creeping into our society and destroying it instead of on the fundamental impossibility of the task.
In a practical sense, I see nothing but problems with this proposal. I also live in Texas, and such legislation would have a huge trickle down effect. How would this affect the fact that I (and thousands of others) have a Texas driver's license with my correct name and gender marker? Would those be rescinded, and how? How does this affect my court order, granted by a Texas judge, that changed my name and gender in the first place? How does this affect birth certificate changes for those who have done their physical transition? Unless someone is willing to fund and carry out statewide blood tests for everyone to determine everyone's original genetic configuration this will be unenforceable.
This reminds me of the Texas constitutional ban on same sex marriage. One of the unintended outcomes was that it made hetero marriages (where one partner is trans) illegal and same sex marriages (where one partner is trans) legal, in both instances where the personal documentation had not yet been changed. And it made marriages to pre-op trans folks entirely legal if a driver's license with the new info was presented to obtain a marriage license, even though the preponderance of (or absence of) penises would, by legal definition, make this an illegal same sex marriage. When confronted with this outcome, the author of the original bill responded by saying, "Yeah, we really didn't see that coming."