One thing we have to keep in mind, and it is a near-universal issue when it comes to a lot of identity-based fear mongering, in deciding your societal virtues you have to make a fundamental trade off between real freedom and security. This is a push-pull process. The only way to be truly "safe" from other people is to have them, and yourself, be very heavily regulated in going about your innocent business. As you open up freedoms for everyone, you run the risk of abuses of that freedom. You can't have it both ways.
We see anxiety over this trade off all the time. Bombings in public places can happen in this country, and many Western societies, because you can't just stop everyone anytime you want and search them. We,collectively, have decided that we're willing to try and police that downside rather than eliminate it and throw out basic freedom of movement along with the bathwater of total security in all public places.
We're having a similar dispute here. The specter is instead some hypothetical possibility of creepy dudes being creepy. Sexual assault and general peeping tom-ery would still be illegal and still be punishable, but the door would be opened slightly wider for it to occur. The argument we're now having is if we want to reduce that risk by some immeasurable amount at the cost of some very awkward life situations for a known small proportion of the population. In effect, taking away their freedom to really live their life as they choose in their own body.
Unfortunately, too many people want to have these kinds of issues both ways. What they really want is to have all their own freedoms and have someone else pay the cost of the increased security and safety. That's the impulse you see when you hear calls for race-based enforcement policies or statutory restroom restrictions. It's trying to have it both ways at someone else's expense. Fundamentally, we all know that isn't right. It's just selfish and mean. And who wants to be selfish and mean?