The short answer is yes, you do. Service animals are often wrongly considered to be pets, but they are actually working animals on the job. Think of them as furry employees who you don’t have to place on payroll.
All jokes aside, service animals are what allow some employees with disabilities to participate equally, and so they will need to be accommodated to the point of undue hardship. There are, however, environments where it would be unsafe to allow a service animal, such as where they may interfere with a health and safety issue. In that case a service animal may not be allowed, but the person would need to be accommodated in other ways.