Now these exemptions may be bad ideas, especially given the terrorist threats we now face. My tentative view would be to oppose them. But the practices of some of these states might suggest that the Florida woman's religious exemption claim isn't as silly as it might at first appear -- especially given that the Florida legislature, in enacting its Religious Freedom Restoration Act, has generally spoken out in favor of religious exemptions.
We got through the Civil War, WWI, WWII, and half the Cold War without any photo ID at all. We can probably survive the WOT.
Note that most photo objectors in the US are Christian rather than Muslim and Muslims (and anyone else) can drive in the US "temporarily" with drivers licenses from foreign countries which may not have any photo or may not have a useful photo.