Firstly, thank you loboris for the Debian image. It made the board actually usable.
About the non-user networking: Apparenly the OrangePi Linux kernel is an Android version, and Android seems to have some restrictions for non-root networking.
I got the normal user (e.g. orangepi) working by creating a group id 3003/aid_inet and adding user(s) to that group. E.g.
# groupadd -g 3003 aid_inet
# usermod -G aid_inet orangepi
Hope this works for you too.