Accrescent, for those who don’t know, is an alternative android app store. They aim to compete directly with the play store, so unlike F-Droid they include both FOSS and proprietary apps. They are also very security focused. They’re still small but I find their approach interesting and their ambition worth supporting.
Unfortunately, as with many FOSS projects, funding is a challenge. If you believe they are worth supporting, please read the linked blog post.
Disclaimer: I’m not affiliated with the project in any way, just a fan trying to raise awareness.
Last I heard, the intention is that users will be able to filter for open-source apps if they want.
I haven’t seen anything warning against proprietary apps specifically. As a minimum, I would hope that they implement an agreement similar to the play store where the app developers are legally bound by the privacy terms in the app description (re data, advertising, etc.). This statement could maybe include an alternative wording for OS vs Proprietary apps? Definitely something to think about.
Edit to add: I can’t comment on 3rd party repositories. Too technical for me.