Universities, and the academics who run them, are the epicenters of left-wing elitism and as such it isn't surprising they think they can negate any laws they feel are unenlightened and not "progressive." Universities make up their own rules about almost everything as if they were soveriegn states and they are shocked when outside visitors to their secluded mini-universe don't comply with their nanny-brained control fantasies.
UVA is public property and is part of the Commonwealth of Virginia. The professorate, administration and population of Charlottesville at large may wish to fantasize that it is in the Commonwealth of Massachusetts but ultimately they are mistaken.
It is my understanding that GMU has a regulation in the state administrative code banning weapons and the issue currently being decided in court is whether they can legally make such a regulation. UVA may have its own rules on guns but to my knowledge they are not part of the state code.
Kicking you out was illegal in my opinion, but you should consult an attorney. If you wanted to challenge UVA you probably should have had 1 or more witnesses accompany you to your appointment with audio recording at least, to prove you didn't threaten anyone, and then refused to leave. If you had been arrested then you would have had a case. Since you left voluntarily, nobody really violated your rights even though what they told you was wrong.