The LGB movement wasn't about taking away from others, it was about giving people the freedom to be in a consensual relationship with like minded people. Whether that was romantic or sexual or both was up to them. Ultimately being LGB hurts absolutely no one.
The trans movement is about solidifying harmful stereotypes about each sex, riding roughshod over women's sex based protections specifically women's and rather oddly considering the origins of the stonewall riots...being incredibly homophobic where being same sex attracted has become a "phobic" declaration. These are all ideas rooted in causing harm and distress, ultimately expressions of aggression and dominance.
If the trans movement was about recognising a need for 3rd space provisions, enabling trans folk to have their medical records reflect their true make up (sex, then whether they are taking cocktails to achieve a more feminine or masculine appearance) then I'd be far more supportive. All other protections are already afforded to them under EA2010.
Truly trans people are suffering because of the people men abusing the kindness intended behind the TWAW idea and claiming trans status to access women at their most vulnerable, or to achieve dominance, e.g. sport
GC folk can't afford to be kind and turn the other cheek. There needs to be consistent vigilance and zero tolerance of trying to delete women as a sex based group. Without that basic identification none of our other rights count for anything.