

Compatibility with Android usually means running DAVx⁵
https://f-droid.org/packages/at.bitfire.davdroid/
A larger package than just CalDAV and CardDAV would be to look into Gromox with Grommunio-DAV.
It’s on my “I should check this out” list, so no personal experience.
https://github.com/grommunio/gromox
https://github.com/grommunio/grommunio-dav
They also have support for Exchange ActiveSync through another optional addon
https://github.com/grommunio/grommunio-sync
Only one I’ve heard of is https://github.com/complexlogic/flex-launcher