The more I think about it, the more I think a humble, sympathetic, non-domineering, non-entryist engagement with the anti-oppression movements springing up around issues of gender identity (i.e. Trans issues) is going to be absolutely crucial for the Left in the coming years.
This isn't just a moral imperative. Sure, the Left must stand with the oppressed. Always. By definition. Otherwise why bother being on the Left? Otherwise, what does 'The Left' mean? But it's also a tactical imperative. The system must be attacked at its weakest points. The righteous and rightful rage felt by many on the axis of Trans oppression is absolutely one of the system's weakest points. It hits people where they live: in their bodies. Bodies are oppressed, disciplined, punished, curtailed, invaded, wounded and even dissected by capitalism... and it behoves the Left to realise that this happens in arenas outside the sites of direct capitalist production. This is one of those things that everyone formally 'gets' and then puts to one side. That's not good enough. Capitalist oppression is total, hegemonic, far-reaching and omnipresent. It is intimately and demonstrably bound up with oppression along lines of personal identity, bodily autonomy, bodily identity, sexual identity, gender, sexuality, and race. This is why intersectionality is a crucial concept that's only going to get more crucial. The task will be to relate all these issues to class. Not so that they can be subsumed, assimilated and/or digested, but so the analysis wielded by the Left can be enlarged, educated, made stronger and more inclusive. That is an end in itself - if we know what our ultimate goal really is.
The good news is that class is as intimately bound up with these things as the Left thinks it is. The bad news is that we have to stress the importance of class without playing 'issue trumps' (i.e. our preferred axis of oppression is more crucial or 'primary' or 'causal' than yours... and, by the way, how dare you stress the issues that hit you where you live before the issues that we think of as theoretically more important???).
But there is more good news. We can stress how capitalism, and thus class exploitation along lines of work and wage exploitation (which is basically just another way of saying 'capitalism'), generates and exacerbates such oppression... for the simple reason that it bloody does; it's the currently regnant form of class society, and we can adduce powerful facts to show how the structure of class society generates sexism, female oppression, gender essentialism, the reduction of people to categories, the reification of socially constructed categories into hegemonic 'facts of life', etc.
That's why this is so good. There isn't anything in there that constitutes new and startling revelation, but it's a great little summary/primer/starting-point, from the perspective of a totally 'on-side' Marxism. I found it so anyway - speaking as someone who personally embraces the elderly Goya's maxim "I'm still learning".
One (related) crucial issue to remember... and here I'd proffer the great work of Silvia Federici... is that the oppression of women is not an optional extra with capitalism, nor is it a by-product of capitalism. It is certainly generated and exacerbated by capitalism (part of the argument the Left needs to make) but is also a precondition of capitalism, intimately bound up with the creation of capitalism, and partly capitalism's parent.
The oppression of women existed before capitalism, because capitalism is a form of class society built on top of previous forms of class society (in Europe, feudalism)... just as the capitalist states are forms adapted from pre-capitalist states. And the rise of capitalism in Europe was absolutely and fundamentally bound up with the further domestication, persecution and economic subjugation of women (see Federici, among others). There really is very little wiggle room here to say that one caused the other. They are two sides of the same coin. And 'causality' or 'primary position' loses its meaning in a truly dialectical (i.e. a truly Marxist) analysis. Besides, its an academic question.
LGBTQIA+ oppression is, once again, related. (BTW: please forgive my using the long acronym as shorthand if you don't like the 'lumping together' effect, or if you're on the other side and worry that trying to be that inclusive accidentally implies that anything not covered is, by definition, not included... and also, please don't construe my raising of LGBTQIA+ oppression as an afterthought.) LGBTQIA+ oppression is intimately connected with the issue of women's oppression, and not in the sense of being a 'product' or 'by-product' or 'side effect' of it, but rather as another aspect of the suffocating enforcement and reification of gender that class society entails, relies upon, and by which it is partly produced.