A lot of anti-CRT rhetoric is clearly trying to use the Marxism link to discredit, out-of-hand, CRT. American politics has always been like that--guilt by association with Socialism. I understand the reflexive instinct to push back against that. But if you try to deny that the links exist, all you're doing is discrediting yourself and others, bolstering those pundits arguments; the links absolutely exist and are substantial. The nuance is that they're not substantial in the ways that the cheap rhetoric implies. (It's like if you took Christianity and replaced Jesus with Santa Claus. You couldn't possible claim the new religion wasn't an offshoot of Christianity, and much of it would be indecipherable without understanding historical Christianity and Jesus. But it would simultaneously be true that the new religion would in some of its most fundamental dimensions be entirely incompatible and incomparable to Christianity.)

If anybody wants to have an informed opinion on these debates, they could do much worse than actually reading Frantz Fanon. IMO CRT begins and ends with Frantz Fanon. If you read his seminal work, Black Skin, White Faces, you've read all you'll ever need to read regarding the ideological underpinnings of not only CRT but much of modern liberal identity politics. I found it a very powerful and enlightening book. (I first read it 20 years ago, before CRT entered mainstream liberal discourse, and before I had any knowledge of CRT as a school of thought or movement. When I did learn of CRT, the parallels to Fanon's ideas were immediately obvious.) But Fanon takes the ideology to its logical conclusion, which is permanent apartheid, and therefore lays bare the stark choice being made when one adopts liberal identity politics. I can't refute Fanon's ultimate conclusion that black-skinned minorities will never be able to find equality among a white-skinned majority (or, presumably, vice-versa if the historical script were flipped), but I choose to believe that there must exist some way to get there; otherwise as Fanon persuasively argues, all identity politics can possibly do is mitigate some of the worst injustices, but ultimately never eradicate the fundamental inequities. And therein lies much of Fanon's motivation for his Marxism advocacy--he thought the only way forward was for black countries to go their own way, and that necessarily involved adopting Marxism as capitalist systems would ultimately benefit the white establishment at the expense of black countries and communities.

Notably, though I've never read any of Malcolm X's works in full, AFAIK he ultimately came to similar (in a very, very rough sense) conclusions as myself. Earlier in his life Malcom X believed it was categorically impossible for black communities to ever live equitably among white majorities. But later on he changed his opinion. It was a choice he made, to choose to believe despite so much evidence to the contrary that there's a path forward offering both diversity and equity, rather than carry on with the dismal axioms that logically pointed to their irreconcilability. Making that choice doesn't require denying all that has happened and continues to happen, it just requires denying a worldview that ultimately makes it inevitable--essentializing racial identity is a self-fulfilling prophecy.

Also, FWIW, modern Marxist scholarship provides some of the most vehement and technical opposition to CRT for precisely the reason you hinted at--replacing class conflict with racial conflict is anathema to Marxism. But when you read that scholarship, it's also instantly obvious that CRT and Marxism use nearly identical language. CRT is indisputably descended from the culture of Marxist scholarship.