Secret societies do exist. Like Free Masonry, Al Qaeda, etc. The thing about secret societies if any are known, it is not that secret. They have their own agenda and they form communities to fulfill those agendas. Christian communities in early days after Christ's death and resurrection lived in secret in catacombs for fear of being persecuted. Every age has it's own secret societies. The Ku Klux Klan (KKK) is a secret society is it not? What about Neo Nazis? There are always obscure societies with bad reputation for what they do. They are mostly known. Not that secret. Free Masons are a real society that keep their business a secret from the common folk.
Now this should not bother Christian people. Aren't Christians not of this world? Don't we labour for a kingdom not of this earth? That's what Jesus preached to us. So, we needn't worry of Secret societies.
The existence of the society, in and of itself, is almost never a secret. You have to use logic, remember how in your logic book the first topic was how to define a word, and then it taught you how to classify the words? A secret is a natural occurrence, oysters secrete pearls, bees secrete honey, and when you go to the gymnasium, your exertions cause your body to sweat. Sweat is a secretion. Secretion is something your body produces, it is the opposite of excretion, which is waste material. The secretion is something useful, or the byproduct of useful work that your body does. One thing you secrete is thought. Thoughts are the secretion of the mind, and your brain does that all day long, one reason why you are here, chatting about Christianity. Literately speaking, this is a secret society, but that is neither here nor there, because every society requires the members to be thinking for them to come together at all, whether formally with paid or free administrative memberships or informally, by way of them all introducing themselves to each other, associating casually and them going their separate ways. What people worry about is that the group is together to plan a criminal activity.