I agree, identity politics is not neo-liberal in origin although it does benefit neo-liberal societies and organisations. I mean, identity politics came out the Left in the US in the 60s - Herbert Marcuse, for one, was highly influential and believed that struggle against Capitalism involved more than the traditional class struggle. Marcuse argued that free speech was of benefit only to the right/ruling class and that the Left should work to suppress speech that they viewed as suppressive.
As for WPUK - I found them very helpful in the early part of the fight against gender ideology but, in my experience of things, after a promising start they petered out somewhat as, to me, it seemed that they weren’t prepared to take the fight to the institutions and organisations (both Left and Right) in the way groups like For Women Scotland, Fair Play UK, and Let Women Speak did. I think Sex Matters are the nearest thing today to the function WPUK fulfilled in the early days of this new feminist awakening.
I wonder if WPUK are disheartened by the fact that the TUs and Labour Party have no intention of listening to them or giving them a seat at the table? If I were a committed trade unionist member, or Labour Party member, I would feel very upset if the movement I’d worked so hard for was treating me as badly as GC women are treated in the political Left.