1. This is not a matter of religious discrimination. No Islamic countries allow women to drive except for Egypt. In Saudi Arabia, they would be pulled from the driver seat and beaten severely for even getting behind the wheel. Even in Egypt, women are required to get their ID photo without their veils on.
2. This is not an Islamic country. If she wants a drivers license, she needs to meet the standards of the law. Given that there is a real need for the authorities to determine that the driver is eligible to drive, and the fact that there is no real privacy violation going on by asking for a photo ID to do so, this woman doesn't have a leg to stand on.