Legal Question in Disability Law in California

You calling them service animals does not make that true. The are service animals entitled to legal protection only if the animal is properly certified as to your need, and it's qualifications and training. If you have that paperwork, and have provided it to the facility, then denial of access and use of the service animal is a violation. However, having a service animal still counts as an animal / pet and the limits on pets apply. So, yes, they can tell you no to another animal as a 'pet'.