Opposition to teaching CRT as fact doesn't mean that we can't teach what MLK believed with complete accuracy.
There are a lot of things that are frustrating about the Critical Race Theory debate, not the least of which that the people on the Right generally don't know what it is and the Left either doesn't know what it is or they lie about what it is.
Let's make something abundantly clear, especially today.
Every human being who is claiming that teaching what MLK really believed is under scrutiny in the CRT debate is an idiot or a liar.
First of all, the earliest concepts of CRT emerged a couple of years before MLK's assassination. There's little evidence that he fully bought into the theory. There's even less evidence that MLK completely agreed with Kimberlé Crenshaw and Derrick Bell.
Still, more importantly, even though there may be some opponents of CRT who do legitimately want to whitewash American history, there's nothing about opposition or criticism of CRT that says that we can't accurately talk about what an influential historical figure believed.
Even if you could prove that MLK was a disciple of CRT, that wouldn't change anything about debating accurate teaching of MLK's beliefs. There's no substantive overlap between criticism of requiring students to draw out privilege charts and worries that we might teach the history of the Civil Rights movement accurately.
I can acknowledge the possibility -- possible likelihood -- that MLK would have been a disciple of CRT. I don't think I'm wrong in pointing out that it's unlikely that he consciously supported CRT even if he was philosophically aligned.