Roman religion was public business before it was private belief. The colleges of pontiffs and augurs were magistracies, the calendar of festivals was a state calendar, and the emperor held the office of pontifex maximus; what mattered was that the rites were performed correctly on behalf of the people, not that anyone felt anything while performing them. On the same principle the empire was hospitable to almost every god it met. Egyptian Isis, Persian Mithras, Anatolian Cybele and Syrian Jupiter Dolichenus all acquired Roman temples and Roman worshippers, and Roger Beck's work on the Mithraic cult shows how thoroughly such a religion could be reimagined inside a Roman idiom.
What the empire required was not exclusive loyalty but participation. Sacrifice to the emperor's genius and to the gods of the state was a civic act, and only two communities refused it. Jews were granted a standing exemption, understood as an ancestral custom of great antiquity; Christians, who could claim no such antiquity and who recruited across the whole population, were not.
Persecution was therefore intermittent and, when it came, administrative. Decius in 250 required every inhabitant to sacrifice and issue a certificate; Valerian struck at clergy and property in 257; and the Great Persecution launched by Diocletian in 303 burned scriptures and demolished churches. None of them lasted, and each produced martyrs whose cults outlived the emperors who made them.