It's definitely not as simple as you're making out. Political speech aside, visas have routinely been cancelled without forewarning for all sorts of reasons historically.

Does someone on a short term visa have the protected right to purchase firearms? Visitors aren't even permitted to get a job without the appropriate type of visa. Being allowed to work is a pretty fundamental right.

I expect there's a difference between the bill of rights and the constitution, and likely further nuance as well.