Most Uber drivers did not "took a job". Uber drivers originally started as self-employed contractors. Part of that is ability to refuse some rides.
Most dog owners have no control over their animals. I have PTSD from dogs, if dog would touch me, I will go into panic attack, and it will not go well for anyone. It is question of safety.
So I have a question for you. As a driver, do I have a right to refuse a drive, if I am concerned that customer will start licking me?