Some folks need to get a grip on the literal translation.
That said, the rhetoric is the same that was spewed throughout Europe in the 1930’s.
The current name, "La Raza", derives from the term "La Raza Cosmica", a concept of Mexicans (specifically those who are of mixed European/Mestizo blood) as a superior race that was arising and would emerge as a world-leading force. The earliest use of the term is from the inter-war period, late 1920s or so. A book was written about it in the 1940s.
A pinch of Nazi ideology, a dab of Marxism, and a great big dollop of racism, all served up as an approved augmentation to national pride, post-Mexican Revolution. The Mexican government has never openly embraced this stuff, but they certainly agree with the anti-capitalist stuff.
The implied meaning is somewhat different than that of the Nazis' "Master Race", but the same time period saw both beliefs arise. More than a coincidence?