I don’t think there is any special legislation affecting who can get out of military service. Basically, we all can, even atheists, as conscientious objectors. There are other rules too, like deferments for going to college, and perhaps there is a missionary deferment (though I didn’t know about one).
@Nullo: Mormonism is dogmatic, and a natural consequence of being dogmatic is contradiction. Hence the notion that someone who is supposedly “pro-life” becomes an ardent Republikan, or the idea that a conservative can simultaneously oppose big government while policing morality. Hell, Mormonism is just plain weird on top of being dogmatic – it’s historically weirder than it is today, given that Romney’s ancestor had numerous wives under a very, uh, ultra-traditional definition of marriage. However, I don’t see any hypocrisy here – if Mormons feel that ministering is more important than their military service, it’s a legitimate theological position – a silly one, perhaps, if you agree with any war, but a legitimate one.