I found the selection policy for NI (Well, it’s for WAG, but I assume it’s the same).
They must hold either an Irish or British citizenship. I think that the CWG are slightly different. I had a quick look at their bylaws, and the only clash I could see if they are dual nationals of two CW nations. I think it’s completely within the rules of the CWG, so FIG is the one with the issue.