Discordianism is a rival cult to the Church of the SubGenius. Planet X is named by conspiracy scientists after the goddess they worship, Eris Discordia. Discordians base their religion on the book Principia Discordia, the number 23, and fnord. Their primary purpose in terms of SubGenii is to destroy the Church of the SubGenius if it gets out of hand. They have both local and nonlocal groups known as cabals.
The original Erisian Cult was in ancient Greece and ancient Rome, with the Greeks worshiping the goddess by her first name Eris and the Romans worshiping her by her last name Discordia. The Erisian Cult of ancient times had the exact same beliefs as modern-day Discordians, but it was persecuted after the dawn of Christianity and became a secret society, known as the Illuminati, for almost 2,000 years. The Illuminati, with their secret handshakes and schemes backed by the goddess Eris herself, gained extraordinary power over the centuries, shaping much of history to their ends.
Then, in the late 1950s, with the publication of the Principia Discordia, a minority of the Illuminati began to go public again with their Erisian Mysteries, rebelling against the rest of the Illuminati, and forming the Discordian religion. After the publication of The Illuminatus! Trilogy by Robert Shea and Robert Anton Wilson in the 1970s, Discordianism became increasingly popular, which alarmed the Illuminati, who have been followers of Eris Discordia for thousands of years, always planning their schemes in secret, never in the open. The Discordians, however, opposed this Conspiracy by the Illuminati, and although they likewise worship Eris Discordia and have the same beliefs, the Discordians are at war with the Illuminati, which keeps Eris Discordia quite amused just as the Trojan War did in ages past.
Since then, the Illuminati have been moving towards establishing a New World Order, while the Discordians have fought them by becoming anarchists and trying to spread chaos and disorder to undermine all authority figures. According to General Public, the Discordians do not realize "that this is EXACTLY what the Illuminati want them to do and that everything is going according to plan and the Conspiracy is in complete control of everything. So while the Discordians try to fight the Conspiracy of the Illuminati, they are actually Conspiracy Dupes and everything they do plays right into the Illuminati's hands. The only way they can ever hope to defeat The Conspiracy is by joining the Church of the SubGenius as ordained ministers, and getting back the Slack The Conspiracy stole away, something which the wisest Discordians such as Robert Anton Wilson have realized and acted upon."
However, J. R. "Bob" Dobbs only let the Church of the SubGenius go public in 1979 because he could depend on the destructive power of Discordians. "If it were not for the Discordians, I never would have set the Church loose on the world -- for I know that they will always be around to DESTROY IT if it gets OUT OF HAND." 
For more on Discordianism there is always Wikipedia and the self-serving Discordia Wikia. Also, here is a video of Robert Anton Wilson, a prominent Discordian and ordained SubGenius minister, discussing Discordianism with Rev. Ivan Stang on the Hour of Slack: