Our shared problem is patriarchy and gender roles. "Why would a man take the inferior role" is behind phobia of gay men and trans women. "Don't let a woman get out of her place, as a sex object for men" is behind phobia of lesbians and trans men. Banding together makes sense.
With the exception of T in sports, unless they compete in their "old" gender. Men and women's bodies are different due to chemical reasons, not just looks. Transgender operations only change the looks, not the chemical reality underneath.
So the outcome of that is obvious : either disallow people to choose gender in sports, or live with the knowledge that all female records will be broken by (ex-)men in no time whatsoever.
The actual scientists, who aren't bigots, have concluded that trans women have no testosterone advantage. After a year or two, a trans woman on testosterone blockers and estrogen (or surgery and estrogen) has the musculature of a woman. Bone mass doesn't change, but that's a disadvantage - more weight to lug around. This is why the olympics and other sporting bodies allow trans women to compete as women.
