Exactly.
And that right does not trump private property rights any more than the right to free speech or to peaceably assemble does.
Do you think a Bible study group has the right to hold its meeting in the entryway of Wal-Mart? ...or that a couple of Jehovah's Witnesses have the right to preach in McDonalds?
Private property rights trump the others, IMO. The reason for this is that you have the choice, as a gun owner, whether or not to enter that property and be disarmed, or have your free speech limited, etc..
If you don't want to give up your gun, don't go there.
Then as a business owner, I can put up a sign that says police or EMT will not be served because they scare my cat.
Open up a restaurant but don’t invite the public.