Has anyone seen the film "Gandhi" (1982)?
This film is more instructive than I can possibly say, in showing an oppressed people how to confront their oppressors.
There is a scene , relatively early in the film, in which Gandhi leads a group of Indians in South Africa who are burning the passes they are forced to carry. This clip doesn't show the consequences of Gandhi's act, merely the act itself. But this shows us how we should confront the bathroom situation.
The way to confront the bathroom situation is: announce the intention to use a particular women's bathroom -- at a mall, for example -- at a particular time, on a particular day. Let the press know. At said day and time, a group of trans women assemble there, and, one at a time, enter -- or attempt to enter -- the women's restroom and use it. The consequences don't matter. If one or more are arrested, the rest continue, until, potentially, all are arrested. If none are arrested, then there is success and the point is made.
The secret to beating the haters is not to confront them on their own ground, but to stand. The better angels of humanity argue for us constantly. Give them a chance to do their work. Be brave. Stand.