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.
Maybe it depends on definitions, but I think if you aren't basing your philosophy in material analysis, you aren't left wing.
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.
But they aren't analysing anything. It's a top down approach where charity is doled out to people who don't pose a threat. It's 'noblesse oblige'. We have seen it all before.
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..
If surrogacy is to benefit men, you can't put a piece of paper between that and any other man who exploits women's reproductive labour. The only difference is the introduction of technology into the process.
If 'right wing' and 'left wing' have any meaning, it has to be about more than adopting a random set of prescribed views.