Agreed, Galaxy. With a few exceptions, I think that many of the things being done under the 'trans' umbrella have been done with good intentions. I think that the reason that TRAs latched onto Stonewall is because most people don't want to repeat the phobic behaviour that gay people faced in the past, and making links with the organisation that did so much for gay people allowed the trans lobby to piggyback on that reluctance. It is also why, IMO, there are so many totally spurious links made between criticism of the trans agenda (as opposed to transpeople) and homophobia.
It also helps that accusations that gender criticism is born of right-wing small-mindedness of the DM variety, mixed with homophobia and a desire for conformity are anathema to most GC people. They are lazy and inaccurate slurs, obviously, but they are the ones reached for when rational argument fails, and are almost guaranteed to be seen as offensive by those on the receiving end.
Unfortunately, there are those who will believe almost anything if it is said often enough, and those of their number who see themselves as kindly, open-minded and tolerant will position themselves on the side of those claiming the moral high ground. They don't see themselves in the way the trans lobby portrays anyone who disagrees, so they automatically agree with their claims (eg TWAW), however obvious it is that they are groundless.
It's a mess, and I hope that now the Tavistock and Mermaids are coming under scrutiny, and now that groups such as the LGB Alliance are separating from Stonewall, clear light will be shone on the trans agenda, and more people will realise that there is no link between the homophobia of old and unrelated concerns about men being able to 'be' women just because they say they are, and that children can be 'born in the wrong body'