I think the confusion is that there is an organization called merely "La Raza" which is extreme extremist. Then, there is the "National Council of La Raza" which is kind of like the NAACP (and still too far to the left for my taste). He is/was a member of one of the state affiliate organizations (the Mexican American something or other) that make up the "national council" part of the "National Council of La Raza". I still don't agree with his affiliation with the NCLR, and I'd have turned down any kind of recognition, endorsement or award from them.
If there is such an organization that's just called "La Raza", it isn't terribly well known, because it doesn't come up in any Google search. What do come up are a bunch of organizations with that phrase in their names (La Raza Unida, La Raza Lawyers Association, etc.). But I'm pretty sure that when you just hear, "La Raza", what's being referred to almost universally is NCLR.