The problem is that this is no longer an ordinary question of definition. I think British opposition leader Keir Starmer gave a definition of woman that deliberately included trans women, and he got plenty of backlash from anti-trans forces. I fear that it will become a 'litmus test' culture war question, and we really don't need more of those.
As to why those supposedly pro-trans people would rather focus on definitions than actual progress in trans rights, I think a major reason is the influence of postmodern philosophy, including queer theory. Which is what I am trying to challenge with my work.