Is google authenticator Private & Secure (Trustworthy) enough to be used for 2StepVerification?

I don't really trust Google at all & mostly try to avoid it.
BUT I wonder if there's some another accessible authenticator app which is more respectful of user privacy & security.

I would like to have another layer of added security other than the password by 2StepAuth for apps like.. IG, Twitter, Orange Website Etc.

Any great recommendations?

amp authenticator google google authenticator privacy