They won't have equal rights if they continue down the path towards criminalizing the act of a trans person reading a story to a child (example from TFA).
I think that is not correct, the example cited in the article is about drag queens performing a 'story hour', not trans people.
I give zero percent odds that the person making this complaint was aware of the distinction between a cisgendered male in a dress and a trans woman in a dress — or the effect that their line of reasoning about an arbitrary person in drag would have on them — but you're right, I understated the demographics under threat.