settlers first arrived in America and their original homelands continued to allow them to vote
That's pretty well it. In the case of early settlers, voting was far from universal and when Italy got its franchise and Poland regained independence, there were strong nationalistic issues involved.
The other problem is that often these people have a sentimental and completely unrealistic idea of the 'homeland
That suits one or two parties often, ones who aren't ashamed to collect votes from people who can5 pronounce the party name.
disillusioned with life in modern America and think they can maintain some kind of Eutopia in their ancestral homelands.
I've noticed that ever since I started using the internet, which was in Poland.
We see it here at PF all the time, with multiple threads over the years. 25 year old pot smoking Kurtan Mucklows in trailers in small town Indiana, very unhappy with their lives, fixating on tenuous ancestry and dreaming of becoming 'kawalers' (which they are anyway in the modern sense) or Winged Hussars, or the moustachioed Hetman of the Podolian Horde.