Kick the big party out of office. If a someone can't hurt you except by getting a someone else to do it, and that person only has the power you give it, deal with that person.

I'm not saying it's easy. I'm saying that the statement "my most immediate concern..." is incorrect. What's more likely: 1) demands from Swedish citizens to the USA actually stopping the USA from using Sweden in its geopolitics? Or 2) Demands from Swedish citizens to the government they empower?

If it's only the extreme fringes, then maybe most people in Sweden simply don't have much of a problem with it or don't care either way, or have more immediately pressing problems to deal with, or something else. Whatever the reason, if you don't like it then your most immediate problem is dealing with the roadblocks to getting your government to stop doing it.