True Contact is only available for Android < 6 (Xperia X is now using Android 7) and I didn’t find a similar app. What I did find is that all fields synchronize when using the “CardDAV-Sync”-App unfortunately this app is not yet open source, so it’s not possible to see how they implemented a work-around.
Add support for Server Name Indication (SSL protocol extension)
Many private servers host multiple domains with different ssl certificates. In order to be able to use davdroid with those servers needs davdroid needs to implement the Server Name Indication instead of the classical SSL protocol: http://wiki.apache.org/httpd/NameBasedSSLVHostsWithSNI
Dup of #9