@BillRM,
The special rule (and you may be reaching a bit, too) is specifically because this is an area covered by our Constitution. Once chess is covered then it, too, can get special rules. But there is a qualitative difference between chess and religion.
And -- I am not talking so much about noise as an issue (which I had thought I had made clear). Rather, that others will hear -- and potentially be influenced, etc. In a country where Congress shall make no law abridging freedom of religion (etc.), and there is a well-established doctrine of the separation of church and state, there can be issues when only one religion gets play in one area,
and the school is state-funded.
I speak as a minority member, for when I attended fifth grade I was one of very few Jews in my school. Others got to miss class for Confirmation classes (which, inexplicably, were held during school hours. This was 1971 or so). I did not. A preference? Perhaps not an intentional one but I have little doubt that no one missing all of those classes (and I recall this going on for at least a good month or so) was bumped down a grade.
By intention was it a preference? Probably not. But it ended up having similar results.
Is having but one club a preference? Not necessarily. But when there is one club, and it is heard, and it is during school hours, and a teacher is there (even if s/he is not participating), and others are walking along and peek or hear what is going on, and hear that their faith is somehow inferior and will not get them into heaven, well, it can have a less than optimal effect, yes?
The solution is, generally, to provide equal time. But that also means that students need to be confident enough to ensure that their needs are being met, and their desires for a club are being fulfilled. Schools, of course, do not have unlimited resources -- not enough rooms, not enough persons to monitor the clubs, etc.
It has the potential to become an enormous mess at best.