Ah, I found the problem: as I suspected, the Treaty of Hidalgo says nothing about whiteness. It only says the people will be citizens of the US. That is related to the reason Mexican-Americans have always been white, but have been treated with the disdain that the Irish, Italians, and other Catholics got.

Irish Americans got accepted the same way that Italian Americans did, by climbing the class ladder. But as you'll see, they're still not very high up that ladder: https://en.wikipedia.org/wiki/List_of_ethnic_groups_in_the_United_States_by_household_income