Having a penis is not how gender is defined, you know. I think she probably gets more say in what her gender is than an unrelated bigot on the internet.
Has anyone reiterated the basic stuff here? That we need to be clear about the distinction between sex and gender
Sex is the biological physiology of your body, determined mostly by the sex-related chromosomes. No surgery in the world yet can change that. So Tara Hudson's sex is male, and will be forever. That's why she is a "transwoman" but not a woman. This is what Germaine Greer says, which apparently was so terrible. She and every biologist in the world ... obviously all of them are promoting transphobia
Gender is the social construction of identity according to ideas about "masculinity" and "femininity". These have tended to be rather oppressive (for both men and women).
At the moment, our society seems stuck in very binary views of what constitutes male and female via gender roles.
The things cited as part of Tara Hudson's working identity suggest hers a very blurred and commodified identity: set up to appeal to heterosexual men who like to have sex with men, but are so homophobic, they prefer that the man they have sex with looks and identifies as a woman. That's not the "norm" of the mtf transwomen I know & work with, who are in most respects perfectly ordinary & normal, just getting on with family life.
I tend to think that a lot of agitation about transgender is actually a product of a) male homophobia, and b) current hypermasculine/hyperfeminine binary gender roles. If we got rid of the oppressive social construction of gender, and let people look and wear whatever they liked, without saying "Oh he wears a dress, he must really be a woman" or "She wears checked flannel shirts & short hair; she's really a man" a lot of people could just get on with their lives
But regardless of her performance of a weird & nastily parodic version of femininity, she's using a hypermasculinised approach to the world in terms of her tendency to serious violence - a far more "masculine" behaviour than it is "feminine". I wonder how they would keep female prisoners safe from violent assault and/or sexual assault?