I don't agree with normal jobs having rules that you need to cut your hair/beard, but this is slightly different.
As 41magsnub mentions, there are practical reasons behind forbidding beards and requiring short hair. Back when the exception was active (1980s), we had far more people in the military and could live with a 50% undeployable rate. Today, if you're in a uniform you need to be deployable. And that means being able to use a gas mask effectively, wear a helmet with your vest, etc...
Besides that, I think part of the problem is the military is in a very uniform concious stage - they want everybody to look the same, and a beard/turban wouldn't be part of being uniform.
Heck, the USAF tightened up and eliminated a lot of the distinctive markings that identified your unit/command on the uniform. Used to be you could tell what Squadron I belonged to, now you're lucky to tell what career field I'm in.