That was only the case in sparsely populated California. If you think racism won't rear it's ugly head when the Americans try for the more populated Mexican states, you're deluding yourself.
I agree with the various statements several commentators have made that once sectional issues were settled, racism shaped what happened to the descedents of Mexicans in the US. Washington wanted to make sure political power was in the hands of Anglos.
This could be done IOTL Mexican Cession because the US got the territory of Mexico that was only sparsely inhabited.
I think it will be much more problematic to do the same things to territories with much larger Mexican population where it is unlikely enough Anglos will immigrate to take over the new state. I am not saying it won't be attempted, but that it'll be much harder to do and could eventually fail. There is only so long a heavily populated territory can be denied statehood without causing a political crisis.
If there is a Civil War, there will be an incredible incentive to make the heavier populated areas of American Mexico states to 1) reward them for staying loyal to the Union, and 2) to encourage young Mexican men to enlist in the Union Army. The exigencies of war can change a lot of things. If so, even having one or two Mexican majority states in Congress is going to give an important voice. In any important close vote, the Mexican representatives can barter their votes to make sure their ethnic compatriots are treated well and additional territories become states.
White identity would change greatly from the 1840s to the 1920s. Irish were considered white by skin color, but culturally were outside the Anglo identity. Mexicans were considered white by census forms from 1850 to 1920. When immigration from eastern and southern Europe increased from 1890s onward, the "swarthy" immigrants from Italy, Greece, and Eastern Europe were often viewed as not quite white. Yet eventually Irish, Italians, Greeks, and others became accepted as being equally white. There was still class distinctions between such ethnic groups until after WWII, but they weren't considered to be racial differences.
In this scenario, I think the vast majority of Mexican-Americans will also become accepted as white. There may be an attempt to distinguish between the "more white" Mexicans than the "more Indian" Mexicans, but that is more likely to be more local and more cultural than actual legal barriers. It'll probably be more of a function of how well the Mexican in question speaks English and adopts more American manners than Spanish.