Compatibility with Android usually means running DAVx⁵
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.
github.com/grommunio/gromox
github.com/grommunio/grommunio-dav

They also have support for Exchange ActiveSync through another optional addon
github.com/grommunio/grommunio-sync