Nationality on Academic CV in USA
I've seen it many times on applications, and it made not a shred of a difference. We did occasionally have Iranian applicants, which is probably the most problematic case, but again it made no difference -- if we wanted to hire someone because of their qualifications, we still did not care about visa issues because that's someone else's problem. For any other nationality, it was a non-issue that wasn't even talked about.

To show you what else doesn't matter: Because I'm German, I put my nationality, birthday, and marital status on my CV for all my postdoc and assistant prof applications. It made no difference: I got invitations to interviews and offers regardless. I don't do it any more because I've learned that that's not typically done in the US. But it really made no difference one way or the other, neither legally nor as far as the hiring committee is concerned.

In summary: You're overthinking the issue :-)