I think this is actually a very interesting question that may not be as easily answered as some think. If for a religious reason, and can be proven as a part of a religious reason, I would think that with past cases on religious liberty, especially within a school setting, that the individual religious rights may be debatable as to the laws. I am not certain, I do know that in the past, the Supreme Court has ruled 5-4 in various cases regarding religious issues in regards to student rights and their free rights to exercise their religious beliefs within a public school setting. With the new supposed conservative nature of the court it is expected that some of these laws, currently being challenged will be over turned. If that is the case, things won’t be as easily decided as we may think.
It should be noted, that none of us reporting on this are lawyers and don’t have the final answer on things like this. Even if lawyers, unless something like this has been challenged in a court setting, then none of us have the pat answer. For those who would argue against the reasoning of challenging something like this, it is a part of what law, and the interpretation of law is for. There is a Constitution, and Bill of Rights for each American Citizen, and as a part of those rights is the right to challenge something that may be deemed as unfair and in fact a violation of Federal rights.
That said, it seems to me, that if the schools were a private institution, funded by private dollars, then at that point they or their governing organizations would be within their rights to establish rules which may, or may not, go against constitutional rights. If however, that organization receives federally funded dollars, then that organization has the responsibility to follow federal law, which may not have been established. I would think that on an issue like this, there has actually been little challenge to the law. Eventually it will happen, and at that point, who knows what the courts would decide. I know one thing, I certainly am not smart enough to make a blanket statement as to the rights of the student, whether he be Muslim, Christian, (yes some Christian religious sects also require a man at 18 years of age to grow a beard, and many of those attend public schools.) or whatever.
My own individual thoughts, are, that whether prayer, or a beard that no laws should be established to prevent the free exercise of ones religious beliefs, not even in a sporting event. The exception is unless there is potential harm that comes about as a result of that practice which I think one would be hard pressed to say is the case a beard would do that. Rules like this over the years, such as hair length has been changed, and I challenge that it could be changed here. I am not certain but I do know that when in High School, in other sports such as football, many had beards. I don’t know if that is the case today or not.
Again, an interesting debate and topic.
Last note, I know the person in question is not an American Citizen, but that doesn't change the possibility of future challenges as there are Muslim American Citizens who participate in sport.