In Indiana, Amish and Mennonites are entitled to get themselves ID cards without photos, because having their picture taken violates their religion. This has not presented a problem for the past several years. However, with Indiana's voter ID law, that might change. The suit is currently up at the Supreme Court, where among the injuries alleged is the violation of the Amish and Mennonite's religious freedoms protected under the First Amendment. As you will read on First Amendment Law Professor's Blog, what the law will require those who have IDs without pictures to do is to vote, then go in to the county election board and sign a sworn affidavit that they object to having their picture taken due to religious reasons. They must do this in order to have their vote counted, and they must do it every time they vote, which the members of the suit allege (and I agree) places an undue burden on them.
Perhaps if the law allowed them to sign the affidavit on the day they voted it might be different, but as it is, this is another good reason to dislike a bad law.