I think the most popular choice is running LineageOS without Gapps.

Not GP, but I assume he doesn't mean a phone with /nothing/ Google on it, but more likely that the phone connects to no Google services and lacks Google Play Services. I do something like this by running AOSP on a Pixel device, which makes my choices of apps that work...less numerous. I'll have to give Jami a try, based on GP's good experience.

AOSP derived ROMs without gapps are pretty much "nothing Google". Unless you count AOSP itself as "Google", which it kind of is I guess, but it's not Google proprietary.