I am not so sure it's about women per se.
I tend to think people like this have an inadequate view of how rights can interact. Or even say, not rights, but just how different individuals and groups have varying interests and needs that may in some cases not all align.
It's a very simplistic view that doesn't really acknowledge that there are pros and cons to every policy and they have to be balanced or accounted for in some way. It's just good vs bad to them. Trans is good so it can't, in their minds, be bad for women.
But people who think this way tend to treat all social and policy issues like that. They have simple minds.