The map in your link suggests that low literacy rates are the result of states with large minority populations and immigrants. For example Iowa and Idaho have much higher literacy rates than say New York or California. Mississippi and Alabama have comparably low literacy rates to New York and California, but I’d hazard a guess that this is a product of their Democrat-voting minority population. Because it’s not like education funding or anything like that otherwise distinguishes North Dakota from Alabama. So I’m not sure what point you’re trying to get across here.
Most immigrants are fully literate in another language and if they can speak broken English are more intellectually accomplished than a huge fraction of Americans who speak only 1 instead of 1.5 or 2 or even more languages.
I'm not convinced that correlation is due to immigrants, unless they mistakenly equated English proficiency to literacy. Anecdotally though, I feel there are a whole lot more homeless people in New York than in Idaho, and maybe that's the reason for the correlation.
The survey linked above relies on English language material to gauge literacy:
> Some of these high county-level percentages stem from high populations of immigrants, whose first language is not English. The PIAAC only assesses English literacy…
Also you can just see this in the chart. The highest literacy rates are in states with the highest native born white American populations, but are otherwise very different in terms of politics (Minnesota and North Dakota). Meanwhile the lowest literacy states are those with large minority or immigrant populations, but again are otherwise very different politically (California and Mississippi).