Business law in Canada makes it possible for businesses to put rules and regulations in place regarding who can come into the store. For example, many shops have a sign on the door saying "No shoes, no shirt, no service." They're allowed to deny service to those who break the rule.
Under this same general guideline, a business can ban animals, and many do. You're not allowed to bring your pet dog into most bars, restaurants, malls and more. Bringing a pet in will likely lead to the management asking you to leave.
The exception to this rule is when the animal is a helper for the person because of a disability. For example, a blind person cannot be denied service or asked to leave because of a seeing-eye dog. Someone in a wheelchair can't be denied service because of a working dog. While these dogs are certainly companions, they also serve functional, necessary roles in their owners' lives, and so they're not considered pets.
It's also illegal for a business owner to attempt to get around this law by charging an unreasonable surcharge for those with animal assistants. The only thing that businesses are allowed to do is to put a policy on the books saying that the owner of the animal has to cover the costs of any damages that the animal causes within the establishment. It's expected that these animals will be well-trained.
Business owners may have a right to run their businesses as they see fit, but this law shows that they can't just impose any regulations at all on their patrons. Owners need to know what limitations exist and how to legally set up a system of rules and regulations.
Source: FIndLaw, "What restrictions can a business impose on customers?," accessed Sep. 07, 2016