No.
But as Cultural Marxist were intended to bring about social, political and even civilizational suicide we shouldn’t expect them to do anything different than they are doing. Indeed, they can still get worse.
Consider: both the Nazis and proper Communist (the soviets behind Cultural Marxism) both believed that they were establishing regimes to last and as a consequence they had a dim view of some of the stuff that Cultural Marxist want. So both were and are evil but they weren’t necessarily insane.
But Cultural Marxism makes for lunatics, madmen who are on a path set for them by those who wanted the societies they are a part of to fail and fall. They are so well equipped for that purpose that even without the Soviet Union (that they were supposed to benefit) still around they are finding new forms of insanity likely unanticipated by the Soviets and are also eagerly, if sometimes cluelessly, serving the role of self destruction for the benefit of others ... notably the likes of the Muslim Brotherhood.
So, no, these people aren’t Nazis. They are too crazy, too focused on the survival of the other and the failure of the “we”. In some ways this makes them worse, especially as their madness intensifies (it seems like it’s a bottomless hole, and they’re accelerating the stupid).
In truth, the Left is the visible emergence of the spirit of antichrist in these lase days - those who, after Christ takes his saints out of here, will usher in the darkest, deadliest, most astonishing seven-year period ever seen on earth (happens in a few decades from now IMO).
Be it Worldwide Islamic Supremacists, Jihadists, Communists, Marxists, Fabian Socialists, AntiFa, Nazis, or whatever name they color themselves, the Left are totalitarian dictators (self-proclaimed and misnamed “Progressives”) striving for Global Totalitarian Government.