Yes, they can.
Trans activists will respond to this with something like “public restrooms, lockerrooms, etc., should not assume that everyone is a cisgender heterosexual and that sexual violence occurs only in the direction if normal attraction, and should provide sufficient privacy and safety for the fact that genser identity, attraction, and sexual violence targets are not determined by sex assigned at birth.”
I would hazard a guess that there are few groups of people who are more aware of, and have spent more energy on considering comprehensive rather than shallow solutions for, this issue than trans activists.
Well, in theory, many things should work. The concerns of women re voiced because, in practice, if these don't work, the consequences can be severe.
And yes, sexual violence dominates in one direction (male -> female/male), that's why we have female-only gyms and other public places, like passenger cars in trains in Asia and other parts of the world. Yes, in theory trains should be safe but in practice sometimes/often they are not, depending on where you live and so on. Saying people who identify as women can enjoy can enter all these safe spaces at will basically destroys all these protections built specifically for women over decades.
How is this argument different from, say, "There are a huge number of men who aren't comfortable with homosexuals seeing their nakedness in public restrooms and changing rooms, and if they won't take medical treatment to get rid of their unnatural attractions, they need to be separated from society"?
Like the whole thing hackers are supposed to be good at is recognizing patterns and coming up with abstractions. How is this not just another instance of the same class of mistreatment Alan Turing suffered?
The difference is that I said the equivalent of the first part of the sentence, whereas the part "and if they won't take medical treatment to get rid of their unnatural attractions, they need to be separated from society" has been added by you, and this is happening regularly in these discussions because people feel the main argument is too weak so they try to add made up things.
If we really want to solve this problem instead of creating confusion, we should really concentrate on the finding out some solutions rather than mischaracterizing the other side. Because, as far as possible solutions go, I haven't heard of many.
But we found a working solution to the previous problem: gay people get to be gay, and people who worry about gay people checking them out in bathrooms and in changing rooms have to deal with it. It's not a balanced solution, in the sense that it didn't make the two sides of that debate equally unhappy, but from all accounts, it seems to work just fine.
The same solution seems like it should apply to the present problem, too. That's why I think these two cases, even though they are different cases, have similarities.
I remember I was in a public restroom in a mall once and a strange man approached me while I was peeing, he was literally looking at my penis. I was very surprised, but didn't feel really threatened, just a bit uncomfortable. But I can imagine being a woman in a similar situation and it doesn't feel like right. The core of the problem is that the victims of vast majority of sexual assaults are women, and for some of them this problem is very real.
It's very hard to argue because it's clear both sides have good arguments: you can't debate someone's feelings. One side has a feeling of being vulnerable for abuse, and the other side feels rejected and misunderstood. It's no wonder that the whole discussion gets out of hand and name calling starts, like "they want to eliminate my existence" where the opposite is often true: the people who feel courageous enough to express their opinion on this dangerous point are the ones who deeply care for others and feel they need to speak out on behalf of those who are too afraid. You can be the most popular writer in the world but it's enough you speak up on this issue and you will be dragged through the mud.