Should Freedom-Loving Americans Fear the Mexican Voter?

At Distributed Republic, Curunir cites this study by Erzo Luttmer and Monica Singhal finding that immigrants' preferences for redistribution tend to be predicted by the average views in their country of origin. They also find a similar but weaker effect on the children of immigrants. Curunir writes:

Now, there are several possible reactions one could take to this finding, assuming it holds up, which is always tricky in social sciences. One is to find that the net benefit of immigration for libertarians is still positive. Another is that free movement of people is simply a basic civil right, consequences be damned (I'm not wholly unsympathetic to this view). A third would be to blame this entire problem in the existence of the state, which strikes me as true but irrelevant (since anarchy isn't coming any time soon, I fail to see why we shouldn't consider how our policies on immigration will effect the world as it currently is).
But what is unacceptable is to just sweep aside concerns over the cultural and political effects of immigration as simple racism. What this study shows us is that it really does matter who constitutes the voting public, and that immigration could easily change the beliefs of the people in ways libertarians will find discomforting.

I think there's some confusion in this response.
First, it is wrong to take a preference for redistribution to say much about liberty at all–even economic liberty. Take the example of Denmark, which has the lowest level of income inequality in the world due to a population with a strong taste for redistibution. But, setting tax rates and government as a percentage of GDP aside, Denmark has a higher level of economic freedom than any country in the world. And the latest Heritage index puts Denmark at 8th in economic freedom, with no really meaningful difference from the U.S's 6th or Canada's 7th.
Of course, nobody in the U.S. is worried about the electoral effect of Danish immigrants. The immigration debate in the U.S. is almost entirely about Mexicans. And I think it's better to not talk in code about abstract foreigners and just face up to the fact that we're talking about people from the much poorer country along the United States' southern border. It is both clarifying and refreshing to talk about the real subject at hand. So what do Mexicans think about redistribution?
Take a look at the World Values Survey. On a 1-10 scale going from “Incomes should be made more equal” to “We need larger income differences as incentives,”  Mexicans average 6.1, the same as Americans. However, Mexican answers tend to cluster toward the ends of the scale, in every income group, while American answers tend to cluster toward the middle, in every income group but the richest (of which there is a very small sample). A larger proportion of poor Mexicans strongly believe there ought to be more inequality than poor Americans. Also, a larger proportion of poor Mexicans strongly believe incomes should be made more equal. On average, poor Mexicans are more pro-redistribution than poor Americans, but less pro-redistribution than poor Canadians. Canadians in general are rather more pro-redistrubution than Americans, but Canada has the same level of economic freedom as the U.S. and arguably more freedom overall. There is, as far as I can tell, little reason to think a large influx of Mexican voters would much change the American median voter's preference for redistribution, which is not in any case a good proxy for a preference for freedom.
But this is all to take for granted Curunir's sadly common confusion between residency and citizenship. It is almost impossible for a low-skilled Mexican to work legally in the U.S. without family ties. There is so much family chain migration and so many “border babies” because that's what it takes to get access to U.S. labor markets.  If we finished the work of Nafta and unified North American labor markets, there would be very little reason to worry about the electoral effects of Mexican immigration, since most Mexicans who come to the U.S. come to work, not to vote, or become American citizens. Labor migration and citizenship are separate issues. If Curunir's worry about diluting the electorate's taste for freedom had force, it would apply to the question of the distribution of citizenships, not the question of openness to foreign workers.