I am not a vet - but I would wager that a vet does have the right not to treat an animal for this. I'd wager they can refuse to treat an animal for any reason. (that doesn't trample human rights)
And in my opinion they should have that right....They studied the diseases and know the risks at different levels.
Obviously any vet can also be a bad vet and/or a bad person - but that's not what we are talking about here.
If the rabies incidence in your area is low a vet will likely take that into consideration.
Personally - I do not think I would give my 14 yr old dog a rabies shot if I thought it would stress the dog out/make the dog ill - UNLESS my vet suggested that in my case (knowing my dog) that this is an overly risky decision.