Well let's look at these two
The great Babylon seems to imply a culture and/or a religion of idolatry and evil. It permeates the whole earth, is secretive and stealthy. It has its hands into everything, has great power. It kills the saints.
The synagogue of Satan has to be the "seat" of Satan. This too is a kingdom, but isn't it likely to be a spiritual kingdom? Or it exists inside people, people with the mind of anti-Christ.
Looking at them this way, it seems to me to cut across all cultures and religions and is in the hearts of people, like a mafia of evil-doers. Just my opinion.
I’m not disagreeing with you. Are you saying that you think those terms are INAPPROPRIATE to use in describing the Catholic Church?