My girlfriend gets harassed by Uber drivers all the time, to the point where she had to switch to using Lyft or call the regular car services here in NYC (which used to be amazing pre-Uber, by the way).
The one time I took Uber Pool in Brooklyn the driver refused to let a black couple into the car, which we all protested and complained about, but nothing came of it.
In New York Uber isn't necessarily safer or less racist, although I'd concede it probably is in other countries.