I would put the burden the other way around. Drivers that have significant animal allergies that reach the threshold of a disability should be provided an accommodation of a separator between the passenger area and the driver area with sufficient air filtration.
Thus, the driver would still be able to pick up passengers that have a service animal even with allergies that extend to the point of being a disability.
I am not a lawyer, but I don't believe that fear of dogs counts as a disability.
That would be another reasonable accommodation. Not assigning driver's to those passengers would be a number of reasonable accommodations. There can be many different reasonable accommodations that can be made for a given problematic circumstance. The burden is on the company to find and implement _a_ reasonable accommodation.
> I am not a lawyer, but I don't believe that fear of dogs counts as a disability.
I don't think a garden variety fear of dogs would could (but IANAL either, and I don't know). I could imagine a case where someone has a genuine phobia of dogs, and is able to get a doctor's genuine medical opinion that a presence in an enclosed vehicle could cause severe anxiety, to the point of causing repeated anxiety or panic attacks. That kind of scenario may well rise to the level of a disability that must be accommodated.
I'm hesitant to make any broad sweeping claims about what should "count" as a workplace disability.
A reasonable accommodation could be that driver's with significant animal allergies don't need to pick up passenger's with dogs. If a significant portion of their driver fleet has significant animal allergies, such that it would significantly negatively impact the response time for passenger's that need dogs, Uber would need to find a different reasonable accommodation.