MLeake, carrying is a behavior, a choice, an action. A business owner can deny you service or access based on this in the same way as if you weren't wearing a shirt and shoes. Not the same as discrimination.
Title II of the Civil Rights Act of 1964 prohibits discrimination in "places of public accommodation" based on race, color, religion, or national origin. The definition of "places of public accommodation" includes hotels, motels, theaters, and restaurants. Now, while a person obviously has no control over his/her race, color, or national origin, the same cannot be said for religion. I choose
to practice Christianity just like other people choose
to practice Judaism, Islam, Buddhism, or even Atheism. As such, religion could be argued to be a behavior itself and thus the argument for carry not being defined as a civil rights issue becomes rather weak.
Also, as MLeake pointed out, a business that is open to the public does not enjoy the same latitude as a person's home or even businesses that are not open to the public such as private clubs. Businesses that are open to the public bear a certain degree of responsibility to provide a reasonably safe environment for the people that they are inviting onto their premises. This is why businesses have to abide by regulations such as fire codes and why they can be found liable for injury or death of their customers if it can be proven that said injury was a result of the business failing to provide a reasonably safe environment for its customers.
By abridging my right to carry a firearm for self-defense without providing adequate security against violent attacks, such businesses put me and my family at unnecessary and, in my view, unreasonable risk when patronizing said establishment. This would be akin to a business barring its customers from bringing fire extinguishers onto its premises while at the same time refusing to have a sprinkler system or fire extinguishers of its own.