Google Play -> F-Droid (New "App Stores" section)

Only open source apps for android (0ver 650 at time of writing). Even if you download an open source app on the Google Play store, there is often advertising and tracking that comes with it. At F-Droid, we do our best to remove all of this stuff before compiling and distributing the apps. Non-Free features are discouraged, and hidden by default. 

https://f-droid.org/about/

I don't have any experience with IOS, but perhaps Cydia is an equivalent tool for that if somebody would like to add that in the future.