Uber, Tinder, and other apps I use require Google Play Services in their latest version. They simply refuse to work without it and there is no web alternative. It's either downgrade to a bug-prone version or use Google Play Services. There is really no privacy on a fully functional Android Phone that isn't just email and phone services - though I guess if you're using Uber and Tinder there is no privacy one way or the other.
You'll find this the case with most location-dependent apps like Uber (to find you) and Tinder (to find people near you). Google nudged most of these apps over to using the proprietary Google Location Services API for this sort of stuff, because of their Wi-Fi triangulation feature.
Whether or not these apps work with MicroG, I don't know.
When I tried Uber (a few months ago) without Play Services, it was working, but without the location feature. So, if you typed an address, it was working as expected.
Uber has a web client. I used it a few times from a laptop when I was without a phone (coincidentally, left it on an uber). Does it not work from mobile devices?
The desktop version doesn't (iirc) but they have a mobile website version, but you have to raise a support ticket manually to get access (or else you get an indistinguishable "permission denied"-like error). It's an odd requirement.... And infitely frustrating :-p
The mobile website works fairly well :-)
I actually thought this might be an avenue for someone like Lyft to excel, but alas they didn't seem any better, iirc...
(not trying to spread FUD, endorse this practice or criticise in anyway, just trying to help the parent comment understand one potential "excuse" for an app "needing" this functionality for a non-obvious use-case.)