I've often wondered if all social justice movements (don't like the term, but can't think of a good replacement) experience this same phenomenon as the women's rights movement, of the movement quickly splintering into camps because of strong internal disagreements of the type we are discussing here.
The reason for that wondering is that I have seen this so many times in the thirty years I have participated in feminist political things and academic feminist stuff and so on.
Initially it made me despair, because the "divide et impera" effect which works against women overall, later I tried to see it as very bright, passionate, and intensely caring women fighting about how to order the things they value in a way which reflects the preferences of themselves, their own hurtful experiences, the smaller groups they represent and so on. I also tried to see the debate as a sign of intellectual vigour and health and growth, especially as authoritarian movements are stifling and ultimately bad for the majority, whether they are left or right or neither in politics.
But I have never grown comfortable with this, though I have grown to accept my own errors and flaws and have grown a thicker carapace over the decades. Still, I did stomp off in hurt tears and rage a few times (as we all give so much of our heart's blood to this and the fights feel like nobody else appreciating that and its costs, the death threats we have received, the earnings we have foregone and so on).
We could achieve so much more if we were willing to accept less-than-perfection, temporary alliances, and halting progress (still progress). But that is very hard to do, in particular because of several things which make the women's rights movement different from almost any other movement I can think of:
It is about something extremely central to most of us, and the lack of it has frightening consequences (think of women and girls in Afghanistan), but 'women' are a giant group, half of all human adult beings, yet split into an enormous number of sub-tribes where our allegiances are for other members of our families, tribes, religions, countries, other political views etc.
It is hard to make bridges across the chasms which are caught by the history of wars, colonialism, class oppression, being mistreated on grounds of sexual orientation or race or religion, and those bridges are fragile. It is partly because of this that the feminist movement is so easy to disrupt, to co-opt for other goals which are laudable but not about the sex-based oppression of women.
None of this is to argue that I don't get involved in these debates or that I don't have opinions on the issues. It's just that I wish I could ignore the chasms which are developing, somehow leap across them when needed, and keep focusing on the very central points, the things which absolutely need to be fixed for any progress to happen. That those central points get support from people who wish them so that progress CANNOT happen does not alter this, as I see more chance for women's rights if 'women' means biological sex rather than some sexist stereotypes about submissive social roles and feminine behaviour and dress.
I would not support or distribute the messages of Matt Walsh in this context, because he is a misogynist who is open in those views. But I can't stop him saying things superficially similar to what gender critical feminists are saying, even though he is saying them for diametrically opposite goals. And I can't stop others from arguing that I must be in league with him, even though I have spent years fighting the views he supports. So I try to ignore it.
I prefer to see the KJK and JCJ in the light of the early suffrage movement which had its radical and moderate wings. The radical wing did help the governments to see the demands of the moderate wing as more reasonable, and may have helped women to get the vote and some other partial improvements. The radical wing might have been able to attain more rights, but it never had the level of support from the wider society which was needed, though perhaps the moderate wing didn't ask enough?
No way of knowing, and we have no real way of knowing what will happen now, either.
(Just wanted to say all that once.)