Out of curiosity: Would someone with dual US/EU citizenship with, say, Sweden be able to get such a clearance without giving it up, or is that a dealbreaker?

You have to be a US citizen and not a citizen or permanent resident of any country that is embargoed for the project. The DOD embargoes run by project (at least where my wife works they manage it that way). You also have to file for permission to travel outside the US. It’s usually not an issue but will be denied if you are traveling to a country that is on the embargo list for the project you’re on.

I don't believe it would be a dealbreaker, but I don't know, as I am only a US citizen.

I think the level of scrutiny would be much higher if you were a dual citizen with a nation the US perceives as an adversary - i.e. Russia, China, Iran, North Korea.

It is a dealbreaker, I have dual citizenship and have been unable to get clearance even before I renewed my non US passport. For the USAF or companies doing private work. It's up to some fat fuck somewhere, his value system, his white knight ideology. Probably sitting at a desk deciding whether you can get paid or not. Maybe it is case by case basis depending on what intel they have on you. They will look underneath your socks too.

not a deal breaker