I wiped an old Android phone, configured it with a dummy Gmail account, and then installed the Uber app there.
So it's a dedicated Uber-only phone with no contacts, no personal data, powered off until I need a ride. It's a giant pain in the ass.
Kinda happy to see this article, it validates my paranoia in some small way.
Now the real question is, why use Uber at all if they're this cavalier with my personal information? Good question, I may not need to power-on my Uber-only phone any more.