Ideas don't remain discrete, they tend to be rather promiscuous. Just as identity politics takes some ideas from Marxist analysis but uses them in a way incompatible with Marxism, they take ideas from other thought traditions and use them in new ways. Particularly from libertarian and neoliberal approaches they take a kind of belief in society as atomic, this is where this business of "rights aren't a pie" comes from for instance.
I think Goosefoot nailed it here.
Trans ideology, and wokeism more generally, is an odd hotchpotch of individualist identity politics and personal actualisation on the one hand, and a nod to structural oppression on the other.
I think the trans ideology stands out among all identity politics as the far and away most influential, and it has very little to do with individual actualisation, in spite of the rhetoric used. It is tremendously successful, because it is a men’s right movement, but without saying so in so many words.
It is therefore entirely structural, as it re-entrenches men’s supreme right to rule and the right to define reality on their terms.
So the labour party at the moment, seemed to have abandoned class-based, structural analyses in favour of individualised identity politics, but is actually engaged in class based warfare, where the classes are men and women, and they have come down firmly on the side of men.
I had been thinking their big mistake was jettisoning structural analysis in favour of identity politics, but it now seems to me that they are very much engaged in structural, sex-class struggle.
I don’t many of them realise this, though.