Even if you believe this, it's still nonsense.
Let's say you believe that trans women are men. And you believe you need to protect cis women. The number of trans women is so vanishingly small, that you've spent a huge amount of energy to prevent the 0.5% case. Legislating always has an opportunity cost, putting forward a bill means not putting forward other bills.
Women suffer domestic violence and sexual violence. 33% of women in the US report experiencing domestic violence. Protect women from that!
Because there are so many ways women suffer in this country, it's very difficult to take on good faith that anyone is protecting them by legislating against trans women. You could choose to solve any problem that affects women orders of magnitude more, but those problems see orders of magnitude fewer bills, if any at all.
No, the data shows this isn't about protecting women, it's about hurting trans people.