You have to overlook the importance of geography and job availability to believe that. Since the areas contiguous to Mexico are those most affected by this and Republican I don't believe your idea is valid. Immigrants can't vote anyway and those from countries other than Mexico are often very conservative and not likely to vote RAT when they become citizens. My neighborhood in Chicago is filled with Polish and Russians who are not much of a problem since they tend to buy property and renovate and repair it so our property values are soaring.
The last thing these mopes from Mexico are thinking of is "remember to tell the coyote I want to go to a Republican area."
Immigrants can't vote anyway and those from countries other than Mexico are often very conservative and not likely to vote RAT when they become citizens.If you think immigrants illegal and legal haven't been voting in the last several elections, you really haven't been paying attention. Further, Hispanic voting patterns do show high levels of RAT voting.
I know many, many Filipinos (my wife among them) and they all vote /will vote Democrat.
They are not told that the Dems believe in abortion on demand, etc.
While they have BS meters just like you and me, they are not able to pick up on the BS because of the cultural differences, or in many cases they just don't know where to look. I expect that for Hispanics it would be the same.