Well, yes, clearly they do.
There is a Change.org petition doing the rounds, supposedly started by "cis" women. For "cis" women to support trans people.
All the TRAs are very excited about how many "cis" women are signing it.
Except - anyone can sign it. I just joined Change.org as Billy Bigballs, and could sign it if I wanted to. All they do is verify your email. I could be a man calling myself Sophie, or Molly, or whatever. Doesn't mean I'm a woman.
So, we've no idea who started it. And they've no idea who is signing it. But to be sure, they'll start trotting it out as some kind of validation/support...