Would Chief Rabbis have authority in their own right, without being poskim?! They may be right or wrong, they may or not consult poskim, but they have a position of authority to make these decisions and that should be respected, unless they are consistently out of line with halakha.
Also, where do Anglicans stand on the spectrum towards A’Z? I presume way below Roman temples, Catholics and Orthodox. So, the issurim of visiting those places may not be at the most severe level.