Ya, and btw, I think it's about 70% or so of Mexicans are "mestizos", which is a mixture of Asian and European genes from way back when, so even if one uses the word "racism" to refer to "race", I would suggest that qualifies.
Mexico's traditional system of defining race was rather convoluted and complicated. It seems they had a word for each race and every possible combination: Peninsulares, Indios, Mestizos, Castizos, Cholos, Pardos, Mulatos, Zambos, etc. Suffice to say, Mexico has quite a diverse population, and there is still a measure of racism, as demonstrated by what happened in Oaxaca a while back.
Even within families, one can see marked differences, since they have both Native and European genes which can vary as to how they turn out.
When it comes to relations between Mexico and the United States, "race" was not really a factor as much as "nationality." It wasn't "white" vs. "black," but "Hispanic" vs. "Anglo" - along with an ongoing border dispute which has lasted more than 170 years. It wouldn't matter if they were white, brown, black, or green - there would still be that border dispute and the rivalry between nationalities, no different than has existed among rival nations in Europe. Just as England and Spain were mortal enemies at one time, their colonial descendants carried it on across the pond.