Federal law has dealt very harshly with non-citizens who claimed to be a a U.S. citizen when that claim wasn’t true. This includes people who tell an employer that they are a U.S. citizen or who registered to vote or who voted. The current state of the law basically bars such people from ever applying for U.S. citizenship after having made such a false declaration.
Sometimes, the error was entirely innocent. We once worked with a man who had been sitting in his apartment one day. A person out registering voters knocked on his door and said, “its time to register to vote.” The man said, “I’m not sure if I am supposed to register – I am not a citizen.” The person said, “well, just fill out the form – if you aren’t a citizen, you won’t get a voter registration card.” Of course, the card was issued and the person had “falsely” claimed to be a U.S. citizen. When he came to us, we told him the seriousness of his actions and told him that he could not apply for citizenship. We were worried that not only would the naturalization application be denied, but that USCIS would try and revoke his green card.