I would absolutely refuse despite the fact it's a service dog, sorry. What if you are legitimately allergic? Are you supposed to dismiss your own health for the sake of discrimination?Service dogs are not pets they are specialy trained to assit people and are protected and legally allowed anywhere with their owner. If you refuse to transport someone with a service dog you are opening your self to a discrimnation suit and de-activation from Uber.
Anyways service dogs are highly trained and will not act like normal pets.