It does seem true though that MLK would have been a vehement opponent of racism towards white people. His words and teachings would not support the idea that "black people can't be racist" and similar modern catechisms. These are harmful concepts that only further entrench white supremacy as people living in fear won't be open to higher minded insight.
I think that's a saying because racism is only harmful when people in positions of power act on their racism and black people traditionally don't have power in this country. If a black judge is only prosecuting white people or anyone else that isn't black, guilty or innocent, that's a case of a black racist. But that situation is way more likely if the judge is white and only prosecuting minorities
I generally only hear people in common conversation complaining that someone told them once that they heard someone say black people can't be racist. I don't think I've seen anyone in the wild claim it with a straight face - because many people use racism and bigotry interchangeably, and it's quite plain that anyone can be a bigot. However:
Racism by sociological definition is something that only the group in power can engage in (paraphrasing) so your problem, like most people who bring this up, is probably:
You heard from someone that someone else said "black people can't be racist" one time, but have probably never actually been told "black people can't be racist." (Which is sort of multiple layers of irony, because if you define the word correctly, they can't, at least generally not in the US.)
and/or
You are using racism and bigotry as synonyms. Anyone can be a bigot, racially prejudiced, etc. Black folks can absolutely be bigoted and racially prejudiced towards others, just like anyone else can.
Here's a snippet of a definition from an into to sociology:
Racism is a stronger type of prejudice and discrimination used to justify inequalities against individuals by maintaining that one racial category is somehow superior or inferior to others; it is a set of practices used by a racial dominant group to maximize advantages for itself by disadvantaging racial minority groups.
The text goes on to say this doesn't preclude racial minorities from being prejudiced, bigots, etc.
And finally, and really this was all that truly needed to be said: In my experience, most of what people complain about online as "racism against white people" turns out to be nothing of the sort, and I'm personally doubtful MLK would have had a sympathetic ear for the common examples I see, either.
"prejudice, discrimination, or antagonism by an individual, community, or institution against a person or people on the basis of their membership in a particular racial or ethnic group, typically one that is a minority or marginalized."
Please get out of here with that "Only people in the dominant group can be racist" mumbo jumbo. That may be the more typical case, but it's not the only one. You (and the author of the sociology textbook you quoted) are EXACTLY the type of people OP was talking about, and that's why you're being downvoted here.
You know how there is a scientific definition of theory that is different than the common usage of theory, and it is really confusing when two people are using the different definitions interchangeably?
Same thing with racism. More than one definition which causes confusion when used interchangeably.
There's more to racism than a dictionary definition, you know that right? People didn't dedicate their lives to study the topic just for the fun of it. The realities of racism from the dominant group (white people in the west) and racism in the marginalized groups are very different. Racism is bad no matter where you fit in that spectrum but the harm done to certain (non-white) groups of people is more severe by several orders of magnitude
What word would you use for the systemic oppression of racial minorities in America?
Do you feel white people experience systemic oppression? In what way?
Which racial group has historically been in control of the large structures in our society (government, large and wealthy corporations)?
If you’re wondering why I’m asking these questions, it’s because I think you’ve missed the point that the poster you’re responding to is making. You seem to be arguing about which words to use instead of noticing the wider topic.
Dictionaries are often treated as the final arbiter in arguments over a word's meaning, but they are not always well suited for settling disputes. The lexicographer's role is to explain how words are (or have been) actually used, not how some may feel that they should be used, and they say nothing about the intrinsic nature of the thing named or described by a word, much less the significance it may have for individuals. When discussing concepts like racism, therefore, it is prudent to recognize that quoting from a dictionary is unlikely to either mollify or persuade the person with whom one is arguing.