In a 5-4 decision written by Justice Ruth Bader Ginsburg, the Supreme Court has refused constitutional protection for 1st Amendment freedom of religion rights for a religious group on a campus at a state college or university to restrict its membership or leadership to those who hold to a statement of faith. Eugene Volokh defends the decision, but I think it's so wrong I don't know where to begin, but at least it's not as bad as it could have been, since (so far, anyway) the decision only covers a minority of cases. It only applies in cases where an institution bans all groups, religious or not, from requiring particular beliefs for membership or leadership. They took no stance on when there's a particular ban on religious groups, but I got the impression that at least Justice Kennedy would have switched to the other side in such cases.
In effect, the Supreme Court has given blanket allowance to a public institution to ban religious groups on campus. Sure, there might be religious groups who have no statement of faith whatsoever, but I know of none. Even Unitarian Universalists have one item in their statement of faith. You must not be an exclusivist or particularist. Someone who holds that Jesus is the only way to salvation could not subscribe to their statement of faith (although an atheist could). Yet if they were to have a requirement for leaders in their group to subscribe to such a statement, the Supreme Court has declared that a university or college could ban them from campus for it.
To be clear, there is a way to have the pretense of being a religious group under such a policy. You could have a statement of faith that you don't follow. What you couldn't do is require your actual members or even your leaders to hold to your statement of faith, not without being forced off-campus. Most student groups I know of do require members and leaders to accept their statement of faith, but they almost always allow participation from anyone, and the statement of faith is never front and center for actual participation in the group. Membership is usually a behind-the-scenes sort of thing, and the leadership selection process is often handled at special leaders' meetings or meetings that don't involve everyone who attends public meetings. So it's not as if these groups require you to hold to a statement of faith to show up at their public meetings and participate. They just require it of voting members and of those who lead the group, e.g. Bible study leaders, the emcee of a public meeting, or the group's president.
It's hard for me to imagine a religious group having any consistent religious identity without requiring at least its leaders to subscribe to a statement of faith. I could imagine a local chapter of Campus Crusade for Christ being infiltrated by a coalition of Muslims, atheists, and other non-Christian people in an effort to undermine the Christian identity of the group. If they wanted the use of campus rooms so that they could actually be, you know, a campus student group, then this policy would require them to allow this. If the influx of non-Christian members became strong enough, what would prevent them from becoming the group and making Campus Crusade for Christ into a group opposed to Christ? It's crazy to think that there isn't at least an as-applied challenge to this policy as unconstitutional in its requirement for viewpoint-neutral membership and leadership of groups who have viewpoint-specific purposes. I would say the same for political groups, either party-affiliated ones like the College Democrats or issue-specific ones like a gay-rights group or a pro-choice group. Imagine if the local chapter of the Sierra Club became overrun by anti-regulation libertarians or advocates of maximal pollution for the sake of short-term human pleasure.
Only in the case of religious groups does this amount to an unconstitutional burden, but as a policy matter it's grossly immoral. It's not the Supreme Court's job to care about that, but it is their job to recognize that this is an infringement of student groups' rights to have a religious identity while being treated like non-viewpoint-specific groups. This decision effectively tolerates suppression of religion on campus when it occurs in an organized group that implements measures to maintain its religious identity by means of a statement of faith. It's no excuse to say that this applies to non-religious viewpoint-specific groups, because it doesn't apply in any meaningful way to non-viewpoint-specific groups. Groups like fraternities will be able to meet on campus. That means there is an as-applied distinction between how religious groups are treated (and it's something necessitated by their religious identity) and how some non-religious groups are treated. I think that's a significant limitation on religious liberty on campus, and thus I'd have to agree with the minority on this one.
The Christian Legal Society still can argue in the Ninth Circuit that policy hasn't been fairly applied to groups but that they've been targeted while other viewpoint-specific groups have not. I have a hard time thinking the Ninth Circuit will support them, but that means it might return to the Supreme Court on that separate issue, and Justice Kennedy would almost certainly be at least open-minded on that claim (and I think Justice Breyer also would, which might make a 6-3 decision). Kennedy has sided with religious groups on similar issues in the past. He just couldn't bring himself to see a viewpoint-neutral requirement as a burden on religion, even though its effect is to ban all religions with any content. Judging by the questions at the oral argument, I could see Christian Legal Society winning the appeal of the further claim they're making that the Supreme Court refused to hear this time around due to its not being raised properly given that it wasn't an issue in the lower courts.