Often times we do not distinguish between 'YOUR private property', such as your home and adjoining land that is only used as your abode and private property which is purchased and owned to accommodate the public. The later includes a business and has the specific and overt purpose of opening to the public for commerce purposes. There is significant differences in these two types of private property. To ignore said differences is a disservice to America and the culture in which we live.
When you open a business there are certain things that you as that property owner agree to with the public, local government and in some cases the federal government. One of the things is that you comply with is the notion of 'public accommodation'. Most frequently we associate this with non discrimination of those that are disabled. Another measure of public accommodation is that it is illegal to discriminate based on race, sex, etc in the course of your business. While possessing a firearm is not (yet) a protected class, I would like to extend my opinion that it will be treated as such in the future as part of the Bill of Rights.