I think transferring a real fear women face (getting raped in or around a bathroom or at least perved on there) from the real aggressor (straight men who assault and harass women) onto a scapegoat who they want to see harmed (trans women) is the how and why.
Using one group’s oppressive fear to do harm to a less powerful group is what fascism is all about, right?
In this way men who rape women are the friends and allies of women like MTG, helping keep women under control and in fear, all while getting to pretend they are protecting women by scapegoating a targeted minority.
That way women will keep getting raped, trans women will keep getting killed, and the underlying power structure that enables this will remain unchallenged (the real goal).