Personally, when it comes to the work place - I believe that the right of self-defense trumps private property if you are open as a business to the public. This is a debate we have had before. However, the 2nd Amend. vs. private property owners is an interesting one and then interacts with all kinds of rights vs. your property. Leads to the protected class arguments.
I only believe in the right of a private property owner or employer to limit the right of reasonable self-defense equipment (no grenades for you), if there is a clear technical danger from the firearm. My test example is not to carry the sidearm by the MRI which can grab them and make them go off!
Now the conflict of property rights, defining gun carriers are protected and the 2nd Amend. is a fun debate - which we've done before.