Can A Muslim attend Brigham Young University?

Answer 1

Muslims are not specifically banned.

Disclaimer: I have no connection whatsoever with BYU.

BYU does not explicitly require that students be members of the LDS church. They do require that incoming students receive an "ecclesiastical endorsement"; for non-LDS members, this is done by a "religious leader" of the student's choice and basically amounts to said religious leader certifying that the prospective student lives a "chaste and virtuous life" and will abide by the BYU Honor Code and adhere to their dress and grooming standards while enrolled as a student.

Answer 2

Yes. I have known of a handful of Muslim students who have attended BYU. In fact, BYU has a Muslim Student Association!

Any student attending BYU is required to adhere by a strict honor code requiring integrity and honesty as well as sexual abstinence (if unmarried), modest clothing, and no alcohol, tobacco, or drug use. This is not an issue for most Muslim students, and in fact is often the reason they chose to apply to BYU. BYU students, regardless of religion, are also required to take a couple classes on Mormon doctrine, and if enough non-Mormons are attending in a specific year, sessions specifically for non-Mormon students will be created. Also, many classes and BYU begin with prayer and you may be expected to participate. You are also required to have endorsement from your religious leader, so your Mosque or Imam will be aware.

Here are some potentially helpful links:

BYU Muslim Student Association
Muslim BYU Students have difficulty with BYU food
Muslim student at BYU Idaho finds experience faith-affirming
Muslim BYU Students get beard exemption