Now, public universities are clearly state actors, and the First Amendment applies. For such organizations, free speech zones are based on the principle that certain "time, place, and manner" restrictions on speech in public areas are Constitutional: http://law2.umkc.edu/faculty/projects/ftrials/conlaw/timepla.... It probably wouldn't have been considered a violation of the First Amendment, even in the founder's day, to charge someone with disturbing the peace for protesting in a residential area in the dead of night, even if they were standing on a public sidewalk.
Universities justify their regulations on "time, place, and manner" grounds, but often stretch that category too far: http://www.thefire.org/misunderstanding-time-place-and-manne... It will be interesting to see further developments in this area. The Supreme Court recently struck down Massachusetts' law banning protests in a 35-foot "buffer zone" around abortion clinics: http://www.npr.org/blogs/thetwo-way/2014/06/26/325806464/sta....
[1] On the flip side there are other people who argue that university grounds are not public forums per se, but are rather private property that happens to be owned by the government. They argue that university campuses are more like a government office building than a public street in that regard. See: http://www.repository.law.indiana.edu/cgi/viewcontent.cgi?ar....
As it notes, people have tried stretching the notion that time, place & manner restrictions are okay into all sorts of impermissible things, like placing unequal burdens on disapproved speech, requiring preapproval to protest, or using the restrictions to stifle speech rather than justifying them as the least restrictive means to fulfill a legitimate purpose.
(Though is leaves out Frisby v. Schultz, the case that held that laws regulating protests can be content neutral, among many other things. http://en.wikipedia.org/wiki/Frisby_v._Schultz)
Note also that it is not particularly relevant that an organization receives public funds. On the one hand, any school (or other organization) operated by a state is also subject to the federal constitution including the First Amendment (of course, this does not cover private schools). And on the other hand, I think your logic stretches too far: I reserve the right to kick you out of my dinner party because I don't like what you're saying. I receive "federal funds" in the form of various tax breaks. If I do actually kick you out, have I violated the First Amendment? I hope not.
The usual rule is that only the government itself (at any level -- or its agents, under certain circumstances) can violate the First Amendment (and almost all of the other amendments, with the notable exception of the 13th). I think it's probably better this way.
Restrictions on political speech in a place and time you can gather with other students to talk about the newest boy band or the unappealing nature of the cafeteria food don't pass constitutional muster for a public institution.
Stifling the speech of someone you categorize as 'crazy' is exactly why the first amendment exists. If everybody wanted to waste their free speech on how cute puppies were, we wouldn't need it.
A number of other universities have also abandoned similar policies. The biggest step is probably the state of Virginia passing legislation designating all outdoor areas of public colleges as public forums: http://www.thefire.org/virginia-bans-unconstitutional-campus....
An organization called FIRE has a great tool that lists speech-restrictive policies at various universities: http://www.thefire.org/spotlight/