I don't think there's much of a correlation there. The fact that the state is still predominantly white should help the GOP, not hurt it.
Most of those people "with continental European ancestry" are probably third, fourth, fifth generation American and the large majority of those have little connection to the old country.
Their ancestors mostly came over in the nineteenth century and worked hard to overcome serious problems without any government handouts. For the most part they embodied the American ethic and they became sound American citizens. Socialism in Europe had little to do with them; it didn't really begin in earnest until after they had established themselves in the US>
Any affinity for socialism that today's descendants from continental Europe have is not connected to their immigrant forebears, but rather has more to do with propaganda they were exposed to in school and are still exposed to via the MSM.
Minnesota’s leftist politics far predates the anti-American propaganda in primary and secondary schools. It is related to European immigrants bringing socialism with them.
http://jcpa.org/dje/articles2/minn3.htm
...Minnesota is the archetypical example of a state informed and permeated by the moralistic political subculture — more so than any other in the Union or perhaps in the world...