I don't know what Marx would say about current identity politics, and I don't think the question is answerable. There is a different question you could ask: could Marxism provide any moral principle that would allow Marx to resist current identity politics? The answer is no.
Marx favoured the rule of the proletariat. As such, he accepted the principle that the right system involves a particular group of people being in charge and controlling everyone else.
This principle is anti-rational. It involves saying that people outside a particular group are always wrong and baking that into the political system so that any criticisms held by those outside the favoured group are ignored except at the whim of the rulers. There can't be any legitimate argument for such a system. So people can only hold it by ignoring criticisms and abandoning the practice of deciding what to do by open-ended critical argument.
Now, suppose somebody comes along and claims that a different group than the proletariat should control everyone else. If you want to reply, your reply can't be that you should take a step back from both positions and consider what principle determines who should be in charge. If you do that, you find that there is no such principle. Rather, that appropriate principle is that you should have institutions that enable the replacement of bad policies and rulers. This is incompatible with both identity politics and Marxism.
Identity politics and Marxism are also both incompatible with free markets. A free market would be set up so that it was easy for people to make agreements where you benefit from providing an agreed good or service, but you can refuse to do so if you're willing to pay a price you agreed on when you formed the agreement. This sort of system has ways of correcting errors in how people act on their ideas. If you come up with a bad idea about how to do something and try to implement it, then you will have to make agreements you can't deliver on and you will have to pay the price. You will run out of resources for implementing the bad idea. Identity politics and Marxism are both opposed to this principle since they want only the favoured group to have the right to dictate what others do.
As such, identity politics and Marxism are both opposed to free markets. Free markets and any other rational political institution are a mortal threat to Marxism and identity politics, so Marxism and identity politics have a problem in common. At the same time Marxists and identity politics people can't both have their favoured group in charge. So at some point both groups either have to change position by rational discussion or coerce the other group into cooperating.
As you may have guessed by now, I think both Marxism and identity politics are evil. My main advice to anyone who holds either position is to reconsider your position. Leaving aside all the other objections, wanting to fight other people all the time sounds like a boring and shitty way to live your life. You should be interested in learning about institutions that facilitate dealign with other people voluntarily, such as free markets.