I found an image of an AR drivers license online. I can’t find ‘Gender’ listed anywhere on it, only ‘Sex’ which is determined by chromosomes.
Traditionally I suppose all U.S. driver’s licenses indicated sex by “M” or “F”, but some now include the “X” option.
Gender was “the grammatical arrangement of nouns, pronouns and adjectives into masculine, feminine, and neuter types in some languages”, but the word got hijacked for other purposes.