Once they told me that the guy self-identifies as female and their policy is to let such people use the bathroom and locker room of their choice, I would've asked if I could have my money back and cancel my membership. If they wouldn't let me, then I would have sued, if that's not in their contract.
Transgenders are not people who are going through a sex change. It is a person of one gender who wants to be the other gender, so dresses that way. He "identifies" as the other gender. But he (it's usually men) is still male.
It's not just about danger. It's about modesty and appropriateness. I think a lot of other women are like me in that I was raised a certain way and am not comfortable going to unisex bathrooms. I do not want to pee in a stall next to a man peeing. I don't want to be adjusting my underwear at the mirror, and a man walks out of the stall with his penis hanging out.
In a women's restroom, and especially in a locker room, women do personal things, like fix underwear, bra straps, use the bathroom, change clothing, do female gabbing, etc. We all have the same parts. Throw a penis into the room, and it all changes. I have a right to use the restroom and locker room without men being around while I change clothing or use the bathroom. Whatever genitalia you have determines the gender you are, and the guy who identifies as a woman is still a male, biologically.
Transgenders aren't the only ones with rights. Other people have rights, too. So if the gym has that policy and they didn't disclose that to me, I should get my money back. I am NOT going to the bathroom and change clothes with men.
Men may feel differently about using the bathroom with women who self-identify as men. I don't know. But I think women are probably a bit more modest about this sort of thing.