Before the Edict of Milan
The Romans tended towards syncretism, seeing the same gods under different names in different places of the Empire, accommodating other Europeans such as the Hellenes, Germans, and Celts, and Semitic and other groups in the Middle East. Under Roman authority, the various national myths most similar to Rome were adopted by analogue into the overall Roman mythos, further cementing Imperial control. Consequently, the Romans were generally tolerant and accommodating towards new deities and the religious experiences of other peoples who formed part of their wider Empire.
The rise of esoteric philosophy
The more philosophical outlook of the Hellenic parts of the Roman empire led to a renaissance of intellectual religious thought around the start of the 2nd century. Writings pseudepigraphically attributed to Hermes Trismegistus, and discussing esoteric philosophy, magic, and alchemy, began to spread from Roman Egypt throughout the empire; while they are difficult to date with precision, these texts are likely to have been redacted between the first and third centuries. Although such hermetica was generally written with the theological aim of spiritual improvement, each text had an anonymous, eclectic, and spontaneous origin, rather than being part of an organised movement.
A more organised form of alatrist henotheistic panentheism emerged in parallel to Hermetism. In the 1st century BC Cicero's friend Nigidius Figulus made an attempt to revive Pythagorean doctrines, an effort that was particularly successful under Apollonius of Tyana in the 1st century; within a century, supernatural powers were being ascribed to Apollonius, and accounts of his life had similarities to those of Jesus. At least one major meeting place for followers of this neopythagoreanism was built in Rome itself, near Porta Maggiore, to a design similar to later Christian churches, though subterranean.
In the 2nd century, Numenius of Apamea sought to fuse additional elements of Platonism into Neopythagoreanism, a direction which Plotinus continued, forming neoplatonism, a religion of theistic monism. Neoplatonism began to be adopted by prominent scholars such as the Christian theologian Origen and the anti-Christian Porphyry. During the rule of Gallienus, the imperial family themselves gave patronage to Plotinus, and encouraged his philosophical activities. Neoplatonism was further developed by Iamblichus, who believed that physical invocations would be able to produce soteriological results, and therefore added religious ritual to the philosophy. Emperor Julian tried to unify traditional Roman religion by mixing it with Iamblichus' form of neoplatonism; the influential Christian thinker Augustine of Hippo lived during this period, and his subsequent writings show heavy neoplatonic influence.
At some time around the first century, the members of the Roman military began to adopt the mystery cult of Mithraism; this sun-god related cult arose from obscure non-Roman origins, and the first surviving reference dates to Plutarch's mention of a 67 BC observation of certain Mediterranean pirates practising it. As the Roman legions gradually moved around, so too Mithraism spread throughout the Roman Empire; in the beginning it was mainly soldiers who followed its precepts, but it was also adopted by freedmen, slaves, and merchants, in the locations where the legions rested, particularly in frontier areas.
Mithraism wasn't exclusive - it was possible and common to follow Mithraism and other cults simultaneously. It eventually became popular within Rome itself, gradually gaining members among the more aristocratic classes, and eventually counting some of the Roman senators as adherents; according to the Augustan History, even the emperor Commodus was a member. Although, for reasons currently unknown, Mithraism completely excluded women, by the third century it had gained a wide following; there are over 100 surviving remains of temples to Mithras, 8 in Rome itself, and 18 in Ostia (Rome's main port), with Rome having over 300 associated Mithraic monuments.
From the reign of Septimius Severus, other, less gender-specific, forms of sun-worship also increased in popularity throughout the Roman Empire.
Elagabalus used his authority to install El-Gabal as the chief deity of the Roman pantheon, merging the god with the Roman sun gods to form Deus Sol Invictus, meaning God - the Undefeated Sun, and making him superior to Jupiter, and assigning either Astarte, Minerva, Urania, or some combination of the three, as El-Gabal's wife. He rode roughshod over other elements of traditional religion, marrying a Vestal Virgin (who were legally required to remain unmarried virgins during their service), and moved the most sacred relics of Roman religion (including the fire of Vesta, the Shields of the Salii, and the Palladium) to a new temple dedicated exclusively to El-Gabal. As much as the religiously conservative senators may have disapproved, the lavish annual public festivals held in El-Gabal's honour found favour among the popular masses, partly on account of the festivals involving the wide distribution of food.
Nearly half a century after Elagabalus, Aurelian came to power. He was a reformer, strengthening the position of the sun-god as the main divinity of the Roman pantheon; he even built a brand new temple, in Rome, dedicated to the deity. It's also thought likely that he may have been responsible for establishing the festival of the day of the birth of the unconquered sun (Dies Natalis Solis Invicti), which was celebrated on December 25, the day when the sun appears to start rising again - four days after having previously reached its lowest point, though the earliest surviving reference to the festival is in the Chronography of 354. He followed the principle of one god, one empire; his intention was to give to all the peoples of the Empire, civilian or soldiers, easterners or westerners, a single god they could believe in without betraying their own gods. Lactantius argued that Aurelian would have outlawed all the other gods if he had had enough time, but Aurelian only managed to hold on to the position of Emperor for five years.
Judaism and Christianity
Imperial tolerance only extended to religions that did not resist Roman authority and would respect Roman gods. Religions that were hostile to the state or any that claimed exclusive rights to religious beliefs and practice were not included and some exclusive Eastern cults were persecuted. Jews were given special privileges owing to their dominance in economy, numbers and dispersal, but this tolerance was balanced unevenly on a thin veneer of Jewish submission. Tolerance of Judaism turned to persecution when collaboration was perceived as ending, see Anti-Judaism in the pre-Christian Roman Empire. Intolerant sects could also persecute each other; Jewish sects like the early Christians were denounced by the Jewish establishment as dangerous provocateurs, according to some interpretations of the Council of Jamnia and the Birkat haMinim. The results included massacres of Christian communities and Jewish nationalist groups.
The early Christian community was perceived at times to be an intrinsically destabilising influence and threat to the peace of Rome, a religio illicita. The pagans who attributed the misfortunes of Rome and its wider Empire to the rise of Christianity, and who could only see a restoration by a return to the old ways, were faced by the Christian Church that had set itself apart from that faith and was unwilling to dilute what it held to be the religion of the "One True God".
The same gods whom the Romans believed had protected and blessed their city and its wider empire during the many centuries they had been worshipped were now demonized by the early Christian Church.