Roman public religion was concerned with getting things done correctly rather than with what anyone thought. A votum was a conditional undertaking: if the god granted what was asked, the payment promised would be made, and its discharge was recorded. Prayers were formulaic and specified which god was addressed and under which name, with catch-all phrasing added in case the right name was not known. If a rite was disturbed by a wrong word, an interruption or an unfavourable sign, it was repeated from the beginning, a procedure called instauratio, and the repetition of entire festivals is recorded.
The aim was the pax deorum, a working peace with the gods on which the community's success was held to depend. Defeat, plague, famine or a run of prodigies indicated that something in the relationship had gone wrong, and the response was procedural: identify the fault, consult the appropriate authority, expiate it. There is little in the public record to suggest the gods were thought to demand moral reform, and there was no scripture setting out what they wanted. What existed was accumulated precedent, kept by the priestly colleges.
Those colleges were organs of the state. The pontifices oversaw the calendar and sacred law, the augurs the taking of auspices, the flamines the cult of individual gods, and the Vestals the fire of Vesta, an unusual lifelong office held by women. Membership was held by men who were also senators, generals and consuls. Julius Caesar held the office of pontifex maximus while pursuing an ordinary political career, and no Roman regarded that as a conflict of interest. Religion was not a separate sphere on which politics might encroach; it was one of the things the state did.