Alright.
This county sits on top of a band of lakes and thus has a different development than the other largely agrian counties in Minnesota, a lot of the economy is based on fishing and lakeside homes. Wouldn't surprise me if that was true even in the 30s. However also the area used to be kind of isolated (not anymore thanks to I-94) and the lakes kind of split it, so it's likely it had the type of enclaves that didn't become fully Anglophone until relatively recently. I know that German-speaking areas survived in Minnesota as late as the 60s, especially in Carver County which was also another one of the three counties to vote for Landon. Actually Carver County used to have a sort of English/German creole that was pretty common, though no one except for maybe a few olds speaks like that anymore. I do know that my grandmother is bilingual though. But these are reasons the county may have resisted realignment with the rest of Minnesota with the New Deal.
Also while the county has an ELCA plurality, it has a significant non-ELCA Lutheran presence making up it appears ~40% of the Lutherans in the county, so the type of progressive Scandinavian Lutheranism probably didn't catch as big here as it did elsewhere. It also appears to be home to a bunch of churches of the "Church of the Lutheran Brethren of America" denomination, a very small Lutheran splinter that isn't particularly conservative (certainly more moderate than WELS and LCMS), but is quite small and has over a third of its reported membership there. That type of population usually points to more isolation which can result in this type of pattern.
Wikipedia also has some interesting info:
So perhaps the local Republican Party made effective use of red-baiting. That bit is quite interesting though, I was not aware of that.