This is almost completely an aside, but the purity spiral equivalents used to be called circular firing squads in that they are doing the job for the enemies of whatever movement we are looking at. Or perhaps the circular firing squads were created partly as a consequence of the desire for no disagreement within the movement?
Feminism is susceptible to this, perhaps more than any other political movement, possibly, because it is about something very central to so much of women's lives and disagreements about the tenets and strategies can feel like some women's concerns being ignored or even attacked and ridiculed.
I used to agonise over this phenomenon, a lot, because splintered movements don't achieve as much as movements which can come together, at least very temporarily, for pragmatic reasons, to achieve one goal at a time. Even if the movement splintered, the new sub-movements should try to keep communication lines open and sometimes come together to support shared goals.
But I have no idea how to fix this tendency toward splintering, except that I have noticed in myself an acceptance of the imperfection of all of us as we grow older and also an ability to decide when a disagreement is about something negotiable for me, and the (very few) cases where it is too fundamental to be ignored. So perhaps discussing this issue in advance and training for how to cope with it might help, by discussing past splintering, what caused it, and how it could have been avoided?
The gender identity ideology is an even more complicated case, because what is loosely viewed as 'gender critical' is really at least two, perhaps three completely different ideological movements. The anti-feminist right-wingers oppose gender identity ideology for reasons which are almost completely opposite to the ones radical feminists have, for instance. So here a certain kind of coming apart is going to happen.