Many, perhaps most, ancient Romans did not belong to any particular sect. The average person in the ancient world would likely worship the local city god, participate in the Roman imperial cult, honor the patron god of a profession, and pay special devotion to whichever deity seems most appealing or likely to help with a particular concern.
But there were also a number of special religious or philosophical groups in the ancient world to which one could belong. For example, an upper-class person might be drawn to a philosophy like Stoicism or Epicureanism, a Roman soldier might be initiated into Mithraism, and a person of any rank might be a special devotee of Dionysus.