Not every state requires citizenship for a driver’s license.
People can get DL with green cards or maybe other resident alien IDs.
My state used to be loose as a goose about getting DLs but they tightened up when people got sick of illegals getting DLs, then driving without insurance and killing people.
Plus many people have noted that green card holders or other resident aliens legally are suppposed to carry papers showing their legal status, so people can carry those (and should) if they have them.