Refugee status is granted only until the game ends. Since the game in our group has been ended, the refugee rule or status does not apply. For example, if a GCA member would have been willing to join CDZ, this would be allowed. In our case, that is not applicable.
Hence, only section 0.3.1 applies and it does clearly specify that double membership is not possible. So, apparently, this means that any user who wishes to stay on a team must not become a member of another team. So, in order to join another team, the member of the CFC team has to cancel the membership first.
My understanding of this is that these games take time and not all sites manage separate games in separate forums like it has been at CFC with MSDG and IDG. Some teams might have only one secure forum with members having access to all games played by the team. For example, if DZ goes to Apo and Rik to CDZ to play in the final part of the game, and during this time frame, a new IDG will start, let's be optimistic and assume it is Civ4 IDG, then both DZ and Rik will not be able to be the CFC team members in this hypothetical Civ4 IDG but will be stuck with Apo and CDZ, respectively.
Certainly, rules can change but this membership rule might remain the same.