[tasn]

EteSync[1] has been around for a few years now. It's fully open source and offers secure, end-to-end encrypted, and privacy respecting sync for your contacts, calendars and tasks. Sounds like what you're looking for...

[1]: https://www.etesync.com/

Disclaimer: I created it.

[dddw]

it's based on davdroid / davx5 ?

[tasn]

Years ago, when it was first created, the code was forked from davdroid, though it diverged quite a bit because the other than the part that interacts with the Android system, they are quite different.