I have a friend who's a relatively (midway, let's say) prominent TRA, and I've been trying for years, without much success, to coax out of him what he actually believes.
What I think his position is: everyone has a gender identity, which most of us don't notice because it's congruent with our biological sex, but it can be really distressing for people when it isn't congruent. So it's a kind of neurological DSD. That hasn't been proven, but let's allow it for the sake of argument.
Following on from that: he believes that this can all be reasonably negotiated by women (the old fashioned definition) budging up and allowing the new exciting women (the ones with cocks and beards) access to women's single sex spaces. At this point he sometimes goes off on a tangent about how Julie Bindel, Alice Sullivan and Alison Bailey (!) are going to patrol toilets policing women for gender conformity.
I don't find this very persuasive. Amongst other things, like a lot of intelligent lefty men, he obviously hasn't given any thought to the question of why women might want single sex spaces.
So this man, who very sincerely identifies as a feminist ally, is in the position where he argues that male-bodied people with trans identities should be able to enter female single sex spaces on their own say so, while female people who might have a problem with that - because of trauma from SA, because of their religious/cultural background, or simply because they don't want penis people in their changing rooms - need to go away and reflect on why they hold these bigoted beliefs and to come back with a resolution to be better and accept male people in female spaces.
Full disclosure: I don't believe that he actually believes all of this. He's got friends who have trans identities and other friends who have transed their kids - and some are mutuals - and has retrofitted an ideological position to fit his social circle.
Is this any different from Tandora's view that a male person's philosophical belief that they were meant to be female trumps a female person's trauma response telling them to get the hell away from a supposedly female space that includes male bodied people?