Apple provides the new “DeviceCheck” framework in iOS 11 to give Uber a “legal” way to do this: https://developer.apple.com/documentation/devicecheck

It allows them to set a bit that permanently “marks” your phone, across installs, while protecting the user from the issues of fingerprinting. In fact, they explicitly call this out as an intended use of the new framework:

> You might use this data to identify devices that have already taken advantage of a promotional offer that you provide, or to flag a device that you've determined to be fraudulent.

Not to say they aren’t still doing something shady, but it’s at least theoretically possible they aren’t.