Alright this is gonna be a bit controversial but
EMOTIONAL SUPPORT ANIMALS SHOULDN'T BE TREATED THE SAME/ HAVE THE SAME RIGHTS AS SERVICE ANIMALS
What I mean by this is that there is a GREAT difference between the two. ONE (service animals) are trained not only to do a specific task to help people with disabilities, health issues, disorders, etc. but are also behaviouraly trained aswell (including: learning to not be distracted by people, other animals or other stimuli, knowing recall and to stay, toilet training, etc.). THE OTHER is not necesarrily trained to do anything and is just there (as stated in the name) for emotional support.
This is the main reason why service dogs are protected and emotional support animals aren't. Service animals are literally TRAINED to be a part of your daily activities in public, and it takes a long time for them to be so.
Emotional support animals are potentially a danger (not neccesarily in the physical danger way, but in the way that they make it easy for people to want to even prohibit THEM in places just like esas) to service animals since they are not trained how to react to different animals they encounter, even if your animal, lets say a dog for this example, get along well with other dogs, they may still distract them from the others duties which is obviously not a good thing. I've heard of many cases where people bring their untrained esas to places and have them behave poorly. This is why people don't want them around. if you can't control your dog to not cause problems for others in say a store, then I fully agree that they can't be there even if you want them to be.
The whole differece is one is trained for these situations and one is not. And the reason esas are banned may not be because of something your one did specifically but what many others did.
Before u come up to me and be like "well i have anxiety and need an esa" THERE ARE SERVICE DOGS FOR SEVERE ANXIETY. They are called Psychiatric Service Dogs and can help with anxiety/panic attacks and help with reminding to take medication.
Having an untrained animal there to support you emotionally might help you, but it may hinder other people and/or service animals.
If you want something to help you with your disabilities, health, severe anxiety, disorders, etc. Consider getting a service animal to help you with your needs, and don't be surprised if you get an emotional support animal, and they are denied in specific places.