Not sure if this is acceptable to you, but Uber has a web app at <https://m.uber.com>. I seem to recall that you have to "request" access in order to use it, but it was an automated rubber-stamp thing. The only downside (besides what you'd expect for a web app vs a native app) is that you can't do fancy things like multiple destinations in one trip, or changing your destination on the fly.

The Lyft equivalent is <https://ride.lyft.com>.