Of course, in the real world, other countries care about American politics in large part because of US foreign policy. The Republicans are the more nationalist of the two major parties, so they're less popular in other countries, just as nationalist parties in other countries are also less popular outside their home nation's borders.
If we're now imagining a scenario in which foreign countries can vote in US elections….how does that work? Is the scenario that they're now US states, and so they have to live with whatever domestic policies the Democrats or Republicans they elect support? In that case, they probably wouldn't care nearly as much about foreign policy as they do now. The whole hypothetical doesn't really make much sense, so not sure how to answer.