The driver’s license issue constitutes a safety concern. In that case it is legitimate to ask the person to uncover their face or head.
When the Daughters of Charity wore coronets, many states refused to give them driver’s licenses because the wings on the coronet blocked the rear view. That was a legitimate safety concern which the Daughters corrected by replacing the Corontet with a smaller cap for driving. It looked like a shower cap. This was before they went to the short blue veil in the picture above.
The same can be said about going through airport security and so forth. Those are safety issues.
Other than that, we have no laws in the US that prohibits religious garb in public.
In New York City Public Schools, Sisters were not allowed wear a habit to teach, but Jewish male teachers were not allowed to wear a Yamulke and other faiths were not allowed to wear their religious garb. Eventually the courts in New York City said that this was unconstitutional.
JR