On Android, Listen Audiobooks [1] is my go to and has been for years. As long as your books are DRM free it's the best UX I've had.

[1]: https://play.google.com/store/apps/details?id=com.acmeandroi...

Looking at LibriVox specifically (linked to by many of the entries in OP), each audiobook has an RSS feed, so I'll just be listening to them in a podcast app. If you have a decent one that keeps track of which "episodes" you've listened to and allows downloading for offline listening (ideally automatically), seems like that should cover the audiobook usecase pretty well.

Smart AudioBook Player on Android works great for me.

I use subsonic to host the audiobooks and play:Sub/AVSub on iOS to listen to them. play:Sub can speed up the books which is very nice for some slower voice actors.

on ios LibriVox doesn't support external files but seems to list many of the free audiobooks from the link above.

In android I use Voice