Yes, some people may be exempt from having their photo taken for a driver's license for religious reasons (i.e. Amish, Christians, Mennonites), depending on the state (see attached PDF). The First Amendment protects the right to practice religion freely, and this may include the right to not have one's photo taken.
NOTE: Photographs may not be waived in Form I-90 (Application to Replace Permanent Resident Card) and Form DS-11 (Passport Form) based on religious or ethnic reasons. If one wears an certain attire, hat, or glasses for religious purposes, submit a signed statement that says it is religious attire worn daily in public. If worn for medical purposes, submit a signed doctor's statement regarding its medical purposes.