I think the problem is that Republicans get them mixed up with another group with a similar name. But that is their loss, of course.
In the context that NCLR uses it, “La Raza” it means “the people,” or “the Hispanic people of the New World”[7] — people of Chicano (i.e. Mexican American) and Mexican descent and the Hispanic world, as well as mestizos who share Native American or national Hispanic heritage.[citation needed]. The concept of inclusiveness was initially promoted by Jose Vasconselos as part of the phrase and title of his essay, "La Raza Cosmica", the mixing of white, black, and native, in the Western Hemisphere. [8] (wikipedia)
When millions of people are demonized because of their heritage, beliefs, or what have you, I cannot see anything wrong with them banding together to fight off that stigma and work to better themselves.
Apparently the Republicans do see a problem with it.