DAVdroid detects read-only calendars and marks them as read-only in the Android calendars provider, i.e. calendar apps should not be able to add events to these calendars. However, this detection is done when the local calendar is created, which is when you add the account.
Can you please delete the DAVdroid account, add it again and see whether the calendar has a “read only” icon next to it? In this case, DAVdroid has detected that the calendar is read-only and should mark it as such.
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.
With google as the only calendar and contacts provider the synchronization worked fine and I never noticed this setting.
I guess Google apps are always allowed to do anything
Good to hear that it now works.