Except, you know, the law would allow a predator to wear a dress and lurk in women's bathrooms. Unlikely, but also not unreasonable fear of true transvestites. That you disagree that it would be a problem worth not passing the law seems to be akin to your disagreement with how resumes are treated -- there's no evidence seemingly for either direction, so neither case is proved or disproved. You can't just insist that things must remain murky in one instance and then demand that they're obviously your way in another. No evidence is no evidence, right?
As others have said, no, no this anti-discrimination law would not in any way aid predators.
1. Current laws already address predatory behaviour.
2. Predators already show they don't care about laws
3. If they do want a "pretext" to be in there, it's easier to pose as a janitor
And yes, it is a completely unreasonable fear. It is transphobia, pure and simple. There has not been a single case of a transgender person using bathroom or locker room anti-discrimination laws in the US to commit or attempt predatory behaviour. There is plenty of evidence of transgender woman being assaulted in men's washrooms.
We. Just. Want. To. Pee.
You are, in fact, statistically more likely to encounter a Republican congressman engaging in nefarious deeds in a bathroom than a transgender person. Should we ban all Republican congressmen from using public bathrooms?
Also, as an aside, "transvestite" is an archaic, and at least mildly offensive, term. If the person has a gender identity different than assigned at birth, they're transgender. If they're simply wearing clothes from a different gender without an associated different gender identity, they're a crossdresser.