We impose a lot of duties on people who are employed in the service of the general public. Humans are messy, unpredictable, inconsistent beings with unique needs so, yes, it is possible that two humans will be a mismatch for each other in the public sphere.
The law, and society in making that law, has generally decided that the right of a person with particular needs--such as a service animal or a carseat--outweigh the rights of someone to ply a trade in a customer-facing role. And, given the level of discrimination that people with those needs experience on a daily basis, I happen to think this is a fair trade-off. The person with the needs may not have a choice, or may have fewer choices, than the service provider.