Whenever I’m asked to provide ID, to make a purchase, rent a car, check into a hotel room etc, I make sure to say “I don’t need this to do something important like vote, why should I give it to you for this?”
It’s amazing how often their eyebrows raise as they are thinking “Wow, that sounds right.” Sometimes they say it too.
Another a question might be “What do you do for those people who say they don’t have ID yet vote? Do you skip seeing their ID?”