That's what EDI is though, and that is it's link to the left.
Classical Marxists, who use the language of Marxism and really believe it's all about class, are matrialts with regard to that, etc, are something of a rarity these days, there is the odd one in academia.
But the activist marxists, people in unions, and most of the marxist parties outside the UK are all now treating class as referring to things other than materialist economics. The groups are build around race or sexuality or any other thing like that, many of them hard to pin down, or in some cases, like sex, they don't fit well into traditional Marxist ideas about abolishing class.
This is the form their arguments take around things like surrogacy, for example. Yes, it will benefit individuals as do all benefits for groups. But the argument for it is based on the idea that surrogacy is the only way to create equity for the class of homosexual men. The argument for race quotas in training courses are about promoting equity between the groups that have been identified as important - "equity seeking groups."
Of course it quickly becomes a thing to become a member of a group like this, or to define new groups, in ways that benefit people who want advantage of some kind. So it creates a push to define all kinds of new inequalities.