Presumably, the relationship would work via the more conservative, traditional ethos and culture of red states encouraging ancestral Mexicans in those states to identify more strongly with the majority rather than distinct from it, as they would tend to in places like California and Illinois.
To flesh out the accuracy of the observation, I looked at all 50 states (to see an accompanying map, click here*). There looks to be something to it, anyway. The correlation between the percentage of ancestral Mexicans who identify as white and McCain's share of the vote in 2008 is a positive but modest .25 (p = .08).
One issue in attempting to discover how voting patterns correlate with various other behaviors or attributes is the fact that blacks are so politically monolithic. The common perception of Mississippi is that it is a patriotic place, but over one-third of its population is black, so despite having the most conservative white population in the country, there are other more moderate states like Alaska and Utah that show up on electoral maps in a deeper shade of red than Mississippi does. The relationship between the percentage of ancestral Mexicans who identify as white and McCain's share of the non-Hispanic white vote, however, is even weaker, at .18 (p = .21).
What about ancestral Mexicans themselves? Unfortunately, state-level data on Hispanic voting patterns are only available for 13 states where the Hispanic population is substantial enough to report on. Despite that limited sample size, though, the relationship is strongest here--the correlation between the percentage of ancestral Mexicans who identify as white and McCain's share of the Hispanic vote is .51 (p = .07). This appears to mesh well with the narrative presented above--the more Hispanics identify with traditional American values, the more likely they are to identify with the majority white population.
By way of the GSS, consider how well this seems to hold up on the individual level. The following table shows, among those of Mexican ancestry living in the US, political orientation by racial self-identification, with blacks excluded and extending back only as far as the year 2000 for contemporary relevance (n = 713):
White ancestral Mexicans are only marginally less liberal than ancestral Mexicans who identify themselves as members of another non-black race are. To the extent that the effect exists, it's pretty weak.
Parenthetically, recall that among the broader American public, people are nearly twice as likely to call themselves conservatives as they are to call themselves liberals. The preceding table shows that among ancestral Mexicans, the conservative and liberal numbers are at parity. Excluding a Cuban population that is decreasing in relevance, Hispanics, irrespective of racial self-conception, are considerably more politically liberal than whites are.
ACS variables used: RACE(100), STATEICP, ANCESTR1(2101, 2102, 2110, 2111, 2130, 2183)
GSS variables used: ETHNIC(17), RACE(1, 3), POLVIEWS(1-3)(4)(5-7)
* North Carolina really stands out as having a low percentage of ancestral Mexicans who racially identify as white. Is there an obvious explanation for why this is the case that I'm unaware of?