Well, that's nice and clear, then!
On the one hand, 'people with prostates' is along the same lines as 'people with a cervix' so at least there is equal language mudling for both sexes.
On the other, the tweets avoiding saying man, transwomen and any other male human show how ludicrous this whole thing is. The exchange Ciao highlighted is 'a woman is anyone who identifies as a woman' in slightly different trminology.
Q. "Which people have prostates, Doctor?"
A. "Anyone who has one! I don’t understand the question. Unless you’ve had it removed or were born without one then I’m talking to you!"