Concealed carry and property rights are compatible
Your property rights end at the surface of my clothes, just as my property rights end at the surface of your clothes. Would I forbid you to come onto my property, assuming I sent out an open invitation otherwise, if you had a pacemaker or an artificial hip? Of course not! Those things are technological enhancements for imperfect human bodies. That is all a gun is. Humans don't have the fangs, claws, or a protective shell for self defense that many other animals have. Most of us do not have the opportunity to become experts at unarmed combat, either. Instead we have a brain that lets us devise tools to make up for that deficiency. To make a rule that a person coming onto your property must leave part of his body behind is crazy and wrong.
A reasonable approach is to forbid certain behaviors: no attacks allowed. And if you break this rule, the other people around you, suitably armed, will stop the attack. The alternative is to encourage massacres like Columbine, Binghamton, and Virginia Tech.
There is much disagreement on this issue among gun owners, and mine is the minority position. That doesn't necessarily mean I am wrong. Here is my train of thought:
Rights don't overlap; two people can't have an equal claim over the same property. No matter where you go, there is a "you-shaped" bubble of your property, with all its rights intact, encasing you. In a free society, absent coercive government, you have absolute rights to your property. If you choose to allow other people to come onto your property (such as for business purposes or private visitation) you are accepting the other people as they are, within their "bubble". Your property rights do not penetrate this bubble around them, just as their property rights don't extend beyond that bubble while they are your guest (unless they brought some other property with them, such as a purse or a jacket). Your only reasonable caveat is that they are expected to behave in certain ways. For instance, not attack other guests/customers nor their host; not steal; and they may be expected to be polite (depending on the circumstances). However, what is inside their clothing is not your business as long as it remains there. Contagions and radiation, and in some cases odors, are things that are reasonable violations of this expectation. Anything else and you are violating the property rights of your invited guests and endangering innocent lives.
You are also assuming responsibility for the safety of your guests or customers if you forbid self-defense. If you fail, you are almost as guilty as the attacker. That, however, is an issue for another time.
