What kind of company was it? I know in my field we don't typically work on any government classified projects, and an employer is not allowed to discriminate (or even ask) about citizenship status. They can't even find out with the I-9 if an employee presents an ID with a SSN card. I do remember applications where I was asked about whether or not I was a current citizen of specific countries, but as far as I know that's not allowed to be used to make a decision - only to determine if someone might need to be vetted further.
I'm not sure what can be done to prove loyalty or at least that people aren't necessarily spies based on national origin. I have an older friend who was born in China, but fled to Taiwan with his family when the nationalist government fell. He's not a fan of communism per se, but he's a huge fan of China. Even back in the 80s, when people asked, he thought of himself as being from China and being Chinese was the biggest part of his identity. But he was senior management at a defense contractor and a naturalized US citizen with access to classified information mostly regarding the work he did. I remember when he made an extended visit to China where he was going to also give a lecture, he had to be briefed on what was acceptable information to share with people there.
I worked in places where it was great because there weren't really any cliques based on national or ethnic origin per se. We would all go out together, talk together, and socialize together. The Indians strangely enough didn't form their own cliques, and the odd thing was that English was usually their common language because they didn't speak each other's native languages. Those who spoke Chinese were from all over - Taiwan, China, Singapore, Hong Kong, and even Macau.
What would be your solution then? Companies being allowed to legally discriminate against people based on national origin? Where would it end? I mean - Israel has tried to gather classified American information surreptitiously through defense contractors and members of the US military.