Here's a way of putting it:
Many people don't hate capitalism in a pure sense because we've gained advantage by it, or saw the dangers of international socialism and or communism.
So how do the left come up with a way to make more people turn on the Capitalist Elite and our History? Use other methods/weapons to achieve their means, including identity politics, and campaigns such as Black Lives Matter.
One thing I will say, however, is that Cultural Marxism is so clever, and so greatly designed, that most people, even many on the left, think it is a ridiculous theory invented by Right Wingers, and give enough no careful consideration. Likewise, many on the Right probably haven't given the theory much thought as they are now being seduced and deceived by ideas like Black Lives Matter, and inadvertently shifting to the Left.
Notice how this happens a lot? We are removing statues of everybody in our past because they were slave owners or slave traders or colonial rulers whatever mistake we can attribute them to. It seems the attack is aimed at individuals for having a poor moral record. But it is actually an attack on capitalism, and attempt to re-write a new world order. These attacks also miss valuable context about the good things in history. We want to pretend history was only full of mass genocide, rape, bigotry, colonialism and every other horror imaginable etc. There is a lot of good in history that gets overlooked because we are so cleverly being deceived to only acknowledge the bad, and then hate our ancestors for it.