Things will get really ugly once you codify special classes citizens and other US persons. It won't happen even though conservative congresspeople have been pushing for it for decades.
I think it's actually similar for US security clearances, though not explicitly codified like that.
IIRC, if you're a dual citizen, you have to renounce the non-American one. Apparently it's not good enough to say "I'll renounce it if you ask," since that's conditional (on them requesting it). You have to renounce it unconditionally. I think that even applies to allied countries (e.g. no US-Canadian dual citizens).
I think the US would also reject a clearance if the applicant had relatives that were in a situation that could be used to exploit them (e.g. foreign nationals, living in a non-friendly country, etc).
Basically, the idea is that you shouldn't have any (discoverable) competing loyalties, and you shouldn't have anything in your life that makes you vulnerable to manipulation.
Disclaimer: I have no actual expertise in this area, but I did spend an afternoon browsing the government website where they described security clearance rejection appeals.
The last U.S. administration quite clearly showed us that clearances mean utterly nothing and are a quickly bypasssble joke in the U.S.
This would have to be a "moving forward policy". Anyone in the US already enjoys protection against discrimination based on place of their birth or race.
In the future, it could be a condition of entry that people acknowledge they are not allowed to work in certain industries, for the government, or universities etc.