If one's religion dictates that they wear a veil in public, and considering that a license photo is a public likeness, then the state has no right to request a public photograph without the veil. The photo isn't the question. Identification by means of a driver's license is an extension of it's purpose, not the purpose in itself. The license indicates that the driver has passed tests indicating the ability to drive, and also paid the regulatory fees and taxes associated.
Proper identification involves much more than simply viewing the photo on a license. The license gives other identifying traits. The picture is simply reinforced evidence that the one carrying the license is or isn't the true licensee.
The true likeness of the lady in public is with a veil. To force a photo without would not yield a true public likeness.
It could be that a driver's license is simply a poor means of identification. Requiring absolute and immediate proof of identity through any means is much too near a police state for me. When a "real" need exists, it's not a driver's license used anyway.
