If they're afraid of dogs they shouldn't drive unknown people for a living, just like someone who's deathly afraid of blood probably won't be a surgeon.
Allergy could be handled by Uber, who should be provided by the driver with a medical certification of the allergy and shouldn't even show that car to the blind customer (if the ADA allows that).
I think the driver shouldn't be able to see that the customer has a service dog, but I agree that they should get a compensation from Uber for doing that ride.