I agree with the principle (and the general vibe) but I think an awful lot of awful people are already looking for an excuse to claim that trans people are just regular people who spontaneously claim to be trans to make a political point. I don’t think it would help to have concrete evidence of Bob MacMan, who looks and dresses like a man and has been living exclusively as a man and showed clear desire to use men’s facilities and men’s prisons when arrested, has claimed to be a trans woman, or vice versa.

For it to not be counter productive, you would have to commit to proving that trans people are very much not just ‘one gender pretending to be the other’, and that would be difficult.

What might be more effective (and honestly, kinda fun) would be like, 8 people all insisting on being arrested at once, or an entire class, or the whole household including ‘granddad’ Dorothy. With everyone committed to doing the conically low/ high voices and playing up the silliest exaggerated charecature (I thought autocorrect was gonna have my back with that word but hey ho) of the opposite gender. You’d get to have some fun, a much lower risk of being placed alone into an opposite gender space, and could really demonstrate the ‘no, this is what it looks like when people just pretend to be the opposite gender’ difference between claiming trans as an act of political defiance - proving their point- and just happening to be a trans person trying to get on with their lives.

Disclaimer - I am not the Joke Police and do not speak for trans people, so pinch of salt required. Also I haven’t seen Spartacus, but I’ve seen the Life of Brain ‘Im the Messiah and so is my wife’ scene, so I feel like I’ve pretty much watched the important bits of Spartacus