You're a law student, right - legally, what parts of this are unconstitutional vis-a-vis the 14th amendment?
Under the Equal Protection Clause of 14th Amendment you need government discrimination, not just discrimination generally (Civil Rights Cases). Students self-segregating in off-campus housing most likely would not be a constitutional issue, and as long as the landlords are not discriminating in who they rent to, federal housing discrimination law would not apply. Public colleges on the other hand are the government, and under the 14th Amendment they may not discriminate on the basis of race unless there is a compelling reason to do so and the discriminatory policy is designed to be as neutral as is possible.
A public college is generally not said to be expressing the viewpoint of any of the student clubs it sanctions on campus, however if the college encourages racist acts from a club, this can be a government act (Rendell-Baker v. Kohn). The student clubs funded by mandatory student fees are protected by the Bill of Rights (Board of Regents v. Southworth; Rosenberger v. Rector). It is generally OK for a lawful group to limit its own membership to preserve the group's message (Hurley v. Irish-American GLB), however it is also OK for public colleges to require its clubs to have non-discriminatory membership policies (Christian Legal Society v. Martinez). Determining whether or not a public college is required to have such a policy under the 14th Amendment is unnecessary because there is probably a federal law violation.
If a student group was having any kind of open meeting where non-members were allowed in, and that meeting was on college property, then enforcing racial segregation would violate the Civil Rights Act. Title III of that law says State governments (and their proxies in college administration) cannot deny someone access to a public place on government property because of their race. So if a group reserved a public room to have an open-to-POC-only meeting, preventing white people from accessing this public place because of their race would be illegal. Assuming this was a public meeting on government property, then the 1st Amendment would not apply, because the organization was not acting to protect its message and instead was merely excluding potential listeners.
The segregated on-campus housing is troublesome, as is the segregated class. Here we are actually dealing with a policy endorsed by the public college. Title VI of the Civil Rights Act prohibits Federal money given to State governments from being used in racially discriminatory ways. Assuming any of the funds which paid for the dorms was federal, then it seems like discrimination here would also be illegal and would result in the college losing its federal funding. Plus it could also be a violation of Title III, since it entails limiting access to a government service on the basis of race. Here you probably could argue the Equal Protection Clause of the 14th Amendment as well. If you are arguing that "Separate but equal" services in public colleges are OK, you must consider every intangible factor imaginable which would likely defeat any segregated housing plan (Sweatt v. Painter). Plus there is no evidence that there is a compelling interest for creating segregated housing, and even if there were the college would also have to show that the program is as inoffensive as was possible.
So in conclusion, I think public colleges would be stupid to promote racial segregation, because these policies violate the Civil Rights Act, and probably the 14th Amendment as well. I find it alarming that some fringe campus crusaders would support technocratic Jim Crow, and the fact that some smaller colleges are buying into it is worse.