Like it or not, this is going to get traction within the majority of the American populace for the following reasons:
1. Despite the media barrage, most Americans do not agree that all the surgery and hormone therapy makes a man or woman. There is no true "transition" from male to female biologically ... medical science proves that.
2. There has always been a slow up tick with regards to prisoner's rights in America. Seems the only time there's money thrown to that issue is when some state wants to load it's coffers by having private industry build a prison/penitentiary in their state, or some corrupt judge starts throwing a lot of people in jail who upon review didn't deserve to be. Otherwise, it's not prime time coverage on MSM.
3. All that has to be said is "your tax dollars are funding all this trans BS in prisons" and you lose the argument to be against what the OP covers.
Whether you are for or against, I doubt anyone can deny or adequately refute what I state here. I would argue that this "movement" will result in the deaths of many of the "trans" inmates. Maybe that will sway the public, but NOT the christo-fascists now running the country.
Just saying.