Guilds, Religions, Cults, Sects, Companies, Corps, Orders, Societies, and probably more, these are all collectively "Associations" within Might & Fealty. These organizations exist somewhere between Houses and Realms, being closer Realms in functionality, but like Houses they can be cross-border entities.
So, what makes them truly different? Associations all work via membership. And Membership can be private. Don't want the lower orders of your sect to know who the high priest is? Then don't tell them. Send a message in confidence, knowing it'll be delivered, by someone of authority, but without your name being associated. Similarly, you can force members to send messages anonymously, where only certain ranks within the association knowing who is who.
But wait, what if your goal is world domination via a cell-based structure of organizations where only the head of the sub-association even knows of the existence of the organization that they're secretly a part of? Well, you should do it. I mean, we won't stop you.
You know what though, that sounds pretty neat, but what about religions? Well, that can all apply to religions if you want, the only particularly different aspect with regards to religions is that characters can choose one as their 'official faith'. Take that how you will.
No restrictions apply on joining associations, unless your Realm or other Associations have some law on it, but who are we to say if they need to know? Largely, these exist to support your imagination, so have some fun with it.