@Hunt I agree with your example of the baseball hats. To me this is analogous to the situation with driver’s licenses. Instead of approving one at a time, you establish a broader rule that does not appear to favor particular groups, such as “You can wear religious headgear, as long as it does not obstruct your face.” Baseball caps are not allowed, but yarmulkes (Jewish), Dastars (Sikh), and colanders (FSM) are allowed. This would keep the school out of the business of approving which religious views are “approved beliefs to them.”
With regard to the Muslim beard, the court ruled that only a 1/2 inch beard is allowed. Furthermore, anyone who wants a beard can claim to also be Muslim and grow one, so essentially anyone can do it.
I would also suggest that the use of the word “need” is very ambiguous. Muslims do not “need” the adhan to practice their religion. Christians do not “need” church bells. None of these issues are preventing someone from practicing their religion.
I agree that the important part of the Duke situation for me is the use of the broadcast system, and the ability of all groups to proselytize publicly. When they just announce the call to prayer from the steps, there is no ambiguity about whether all groups also have the right to announce their views in the same way since it is not being electronically broadcast. I also assume that a student of any religion is free to stand in front of the chapel and proselytize, so to that is equal. If what they are saying and the way they are saying it are allowed for anyone, who could reasonably object?