The Voting Rights Act of 1965 prohibits states from imposing any "voting qualification or prerequisite to voting, or standard, practice, or procedure to deny or abridge the right of any citizen of the United States to vote on account of race or color."
So how does this apply to any laws aimed at NON citizens?
While poll taxes and literacy tests arguably applied only to blacks particularly in their enforcement, it is hard to see how requiring an ID card would. Unless you could show that this procedure was enforced only against a certain race or color. There is no evidence of that as the law is written or implemented.