Uber has made some effort to accommodate passengers with special needs, but it certainly hasn't been perfect: in 2014, the National Federation of the Blind's California branch sued Uber for denying rides to poor-sighted passengers with guide dogs and other service animals. However, it might soon make amends. The ridesharing company has proposed a settlement in that lawsuit that would protect your ability to take service animals with you on trips. Drivers would get in-app pop-ups and emails reminding them of their duty to carry your companion, and there would be a formal policy that bans drivers if they're caught rejecting passengers with animal helpers.
The settlement won't do much damage to Uber's bottom line if it's approved -- the company will pay just $225,000 over the space of 3 years. With that said, it could do a lot to protect passengers. Even if drivers aren't immediately aware of their obligations, you'll have direct recourse if they ever threaten to cancel your trip.