IMHO, it has more to do with a 'photo' being a sense of a display of pride, however they do at times use photos. My limited understanding is that different groups have different dictates and interpretations.
See
http://www.amishnews.com/amisharticles/amishand photos.htm
I think, though, that a sincerely held religious belief should take precedence over a governmental requirement that really serves no purpose. Since they have been exempt, and are also exempt from some federal photo requirements, the State of Illinois should, IMHO, just drop the issue. Does the governmental need for the photo trump religious expression? In this case, I don't believe it does.
Interesting read. Although I do personally chafe at some of the requirements imposed by our servants, methinks there must be some balance; otherwise, at which point does someone's personal beliefs take on the mantle of 'religion'?
Does one person's deeply held belief qualify? What if two hold the same? Is it then now a religion, or does it remain a personal preference? How many does it take, and who decides that number, before it becomes a 'religious' tenant? How many people followed Koresh? Apparently they had some deep seated beliefs regarding religion and automatic weapons. I know that's a bit extreme, but I'm offering a point.
Remembering that Abram held an unpopular, monotheistic view, he was one man. From one came three great religions; Judaism, Christianity and Islam. So, the deeply held beliefs of one are obviously significant.
How do we sort out the Koreshes and the like, from 'legitimate' religions? Again, who decides?
Alas, but I am not Solomon; I cannot say. But, I ponder these mysteries.