Twidere is a very nice F/LOSS Twitter client available through FDroid:

https://f-droid.org/en/packages/org.mariotaku.twidere/

Issue:

Trying to login to Twitter with it gives “Incorrect API Settings” message

Fix:

Remove the account. Somehow you’ll get to an Advanced > Network > API settings screen that has a Load Defaults button. Tap it. When it’s finished, go to Accounts and add your account back.

Question:

How to log out of Twitter from Twidhere?

Answer:

Remove the account. Not at all intuitive, but that’s how it works.