I think it has two aims. Dogwhistle politics is the sending of coded messages embedded in otherwise unremarkable discourse. So words, phrases, images or gestures which are meaningful to a particular set of people.
The term is often used when talking about racism or white supremacism or class.
So one effect of using it in the sense of hidden transphobia, is to create implied links between gender critical discourse and racism, white supremacism and fascism. There’s been a recent push to characterise radical feminism as white supremacism and gender critical thinkers as the plague carriers of a new colonialism.
The other effect, more generally, is to allow pretty much anything to be characterised as transphobia.
Your dog puts her head up because she heard a sound you couldn’t.
A TRA will say, “that’s transphobia!” “That’s not how I heard it”, the rest of us say. “Well, I can tell because I know these things”, and we accept that we just missed the reference or didn’t understand the code.
“Transphobic”, we nod and soon enough anyone speaking outside the approved script is deemed transphobic.
We must push back against the policing of language in the service of a powerful minority.