It's worth remembering if considering a vote for the Greens, that there's obviously no chance whatsoever of them forming government, or at this stage even having any significant minority power. So it's not like the TWAW idiocy is actually going to affect legislation of have any practical consequences.
In this sense it's different from the question of whether to tolerate Labour's position on trans rights and vote for them, because there you're having to tolerate actual laws potentially being passed.
Obviously it's not ideal, and noone wants to vote for a party with policies in one area that they find offensive, out of principle. But I agree with most everything else the Greens stand for - and having lost all faith in Labour, contributing to the long-term growth of Green support is the only modest way I have to use my left wing vote. If that ends up amounting to actual political power of some kind 20 years from now, then the trans debate will have moved on by then anyway.