Orthodox was a word used to describe the traditional form of a religion or other belief.
Vedek Winn Adami came from an orthodox spiritual order of Bajorans. In 2369, she and other similarly believing Bajorans came to Deep Space 9 to protest the science curriculum at Keiko O'Brien's school. When Odo explained this to Quark, he said he'd need twice as many dabo girls working at Quark's, as the '"spiritual types" loved them. (DS9: "In the Hands of the Prophets")
In 2370, Jaro Essa tried to win Winn to his side, as they both believed in a return to orthodox values. (DS9: "The Circle")
In 2373, Elias Giger described Jake Sisko and Nog as "soulless minions of orthodoxy", before being assured they were not among those who constantly bothered him. According to Giger, these individuals refused to follow up on Doctor Bathkin's work on what would become the cellular regeneration and entertainment chamber. When Odo could find no record of Giger on the station, Nog suggested that the minions had caught up to him. Later, Giger accused them of handing him over to the minions (aka Weyoun 5). (DS9: "In the Cards")