The best piece of info I can see is found here:

Brigham Young University, Brigham Young University—Idaho, Brigham Young University—Hawaii, and LDS Business College exist to provide an education consistent with the religious and family values taught by The Church of Jesus Christ of Latter-day Saints. We prefer to admit members of the Church in good standing but will not unlawfully discriminate against applicants based upon gender, race, creed, religion, national origin, age, or disability who meet the requirements, who agree to abide by the Honor Code and Dress and Grooming Standards, and who are otherwise qualified based upon available space.

Students must be in good Honor Code standing to be admitted to BYU and must continue to abide by the Honor Code and Dress and Grooming Standards while attending BYU, whether on or off campus. An applicant who is currently excommunicated or disfellowshipped from, on probation with, or voluntarily disaffiliated from The Church of Jesus Christ of Latter-day Saints is inadmissible until reinstated to full fellowship.

The quote under "good Honor Code standing" contains a piece called "Withdrawn Ecclesiastical Endorsement" that outlines the policy:

A student's endorsement may be withdrawn at any time if the ecclesiastical leader determines that the student is no longer eligible for the endorsement. If an endorsement is withdrawn, no confessional information is exchanged without authorization from the student. Students without a current endorsement are not in good Honor Code standing and must discontinue enrollment. Students who are not in good Honor Code standing are not eligible for graduation, even if they have otherwise completed all necessary coursework. Excommunication, disfellowshipment, or disaffiliation from The Church of Jesus Christ of Latter-day Saints automatically results in the withdrawal of the student's ecclesiastical endorsement and the loss of good Honor Code standing. Disaffiliation is defined for purposes of this policy as removal of an individual's name from the official records of the Church.

Now comes the opinion part. Please remember that we don't downvote just because we disagree (unless you suck).

I don't see this movement being successful. The standards of conduct might annoy some folks, but it is true that A. BYU is a Church-owned private school that is entitled to uphold these standards on account of the fact that it is a private school and B. Students are aware of the contract that exists for them when they agree to live the honor code when they choose to attend here. Legally, BYU has the right to expel students who fail to live their end of the contract, regardless of whether there is opposition to it.