Syncing across firewall
I do not really have problem. But I found a modified behavior of DAVDroid somewhere in the past, probably in the course of 2016, which makes syncing complicated now.
I use a Samsung phone, original firmware, Android 6x, rooted. Rooting was necessary in order to install a firewall. Until somewhere in 2016, it was sufficient to open the firewall for DAVDroid (I can choose for which processes/apps to open the firewall). It is not so anymore. Opening the firewall for DAVDroid only does not allow for synchronization (no error messages from DAVDroid). I did not have the time yet to puzzle out for which other process/app I have to open the firewall additionally. Therefore, I deactivate the complete firewall for a short time, when I want to synchronize. This is poor.
Which (system?) process is used by DAVDroid additionally to accomplish synchronization?
Why did it work before?
DAVdroid uses okhttp, which uses the standard Java TCP/IP stack. Network traffic for CalDAV/CardDAV synchronization is only managed by DAVdroid, so you shouldn't have to unblock any other processes.
Please note that this is not a DAVdroid problem, so I suggest to ask your firewall vendor for additional assistance.