No, they're secret.
Sorry; it's a very old joke! Anyway...
Each of the temples - and for all I know, any of the social entities in the Five Empires - have factions that seek to promote one or another agenda. Some are very public, and some try very hard to stay as covert as possible. Some have a lot of followers and power, and some do not.
I am a card-carrying, dues-paying, member-in-good-standing follower of the Incandescent Blaze Society of the Temple of Vimuhla; we are devoted to the restoration of the world-dominating theocracy of the Temple that existed under the Dragon Lords. We have members in all the Flame-worshipping clans, and also in all of the Legions devoted to Lord Vimuhla. We are A Power Upon The Land, as we'll me more then happy to explain to you - some of our more fanatic members are really boring at parties, I should warn you. We're out to expand our role in society and government, and to increase the power of the Temple. (And get a few nice perks along the way, if possible. It's good to be the High Priest, assuming that that Chirine guy doesn't kill you out of hand for dipping into the Temple's till...)
And like any properly organized secret society, we have our conventions, conferences, seminars, management retreats, annual meetings, reunions, hospitality suites, social events, team-building exercises, and out-and-out junkets to the better guesthouses. Occasionally, we'll throw a war or two to keep in practice, but that's all part of the fun.
I can hear you ask "But, how does that work in society?"
We take the very long view. It may take generations to reestablish our supremacy, but we'll get there - eventually. In the mean time, we have adventures, wars, expeditions, and such-like to keep us busy.
These sorts of societies are part of the fabric of political life, and are very common. None are looked down on, except by their opponents. It's usually a matter of pride that one is in a secret society, and there's a lot of name-dropping and wearing of the particular society's unique glyph. Generally, unless the member of the society is on the business of the group, and needs to be discreet, it's pretty obvious what they belong to, and the societies are usually pretty up-front with each other in their dealings.
For example, my First Concubine / second wife (a very nice and pleasant lady) is a priestess of the Temple of Ksarul, and a member of (I think; I really don't ask, 'cause it's supposed to be a secret) the Refulgent Blue Light Society. Our two secret societies are directly opposed to each other, but as in all things Tsolyani a certain practicality prevails; I do reports on her nefarious activities, and she does reports on mine. We each get a small stipend and our expenses for all this skullduggery and intrigue, which is nice as it helps with the costs of having a large family. We always make sure that each of our secret societies get something out of our adventures, too, as it keeps everybody happy.
More? Less? What else can I tell you? Phil covered this pretty extensively in the Sourcebook, as I recall...
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