AnkiDroid: https://f-droid.org/packages/com.ichi2.anki/

Privacy Policy: https://github.com/ankidroid/Anki-Android/wiki/Privacy-Polic...

From the F-Droid description:

Opt-in synchronization uses the non-free AnkiWeb service by default, but this can be changed in the settings to use, for example, an instance of the unofficial Anki Sync Server).

Opt-in / off-by-default crash reporting will send data to a private / AnkiDroid open source team controlled crash reporting server if enabled. This data is only used to help fix crash bugs.

Opt-in / off-by-default analytics will send data to Google Analytics via an an open-source implementation of the analytics API if enabled. This data is only used to focus developer efforts on popular features.

> The issue is: I'm sick and tired of apps that want your web credentials. I want an app that doesn't share anything about me. Completely local.

Anki does not require your web credentials, so it's very well suited for you!

You can create an account if you want to sync your decks between computers or to your phone. It is not necessary or required.

You can also run your own sync server so you can get the benefit of multi-device syncing without needing to use the free provided service.

https://docs.ankiweb.net/sync-server.html

Excellent. Thanks.