There's No Place Like Rome
Even though Rhodius believed the gods had abandoned them, not every soldier or camp follower agreed. In the years that followed, many continued worshiping their gods in secret, both out of respect for Rhodius and for fear that they too would be executed.
As there were an unusually large number of cavalrymen, small shrines to Epona were a regular feature in stables. The shrines would consist of a small picture carved into the main support pillar of the roof of the stable, with a table holding fresh roses and libation bowls of wine below it.
Small shrines to appease numina (spirits) could be found in most homes.
… The more common numina were found in every household. They included the lares, who guarded the home and the land, the penates, guardians of the storerooms and the food, and Vesta, the female numen of the fireplace. A shrine to all three was usually kept somewhere in every house, and small offerings of food were given to them. Additionally, a family spirit, the genius, was also given homage… These spirits required small offerings: to neglect them was supposed to bring bad luck.”1
In the old world, Jupiter was worshiped as a god of loyalty. Because Rhodius saw their transportation to the strange new land as abandonment, worship of Jupiter as head of the gods fell out of fashion.
Sol Mithras, a combination of the eastern god Sol Invictus and the Persian god Mithras, gained a small following when those familiar with the religions began to allow female worshipers and dropped the practice of animal sacrifice. The constant struggle against evil and the promise of a life after death was promising to those suffering in this new land.
The philosophy of Stoicism gained a strong hold on the people. Rhodius Rex was an adamant Stoic, and sought to impress upon his people the need to handle their new lives with calm endurance and acceptance. Rumors were spread that his distaste for religion was the cause of the priests’ execution, yet calmer heads claimed that it was to halt the grip of terror the call for human sacrifice had sparked.
Conversely, Rhodius Rex was deified shortly after his death by an unanimous Senate vote.
There are no state ran temples or sponsored religions, though temples do exist throughout the Empire. They are usually small, privately-funded buildings and do not allow just anyone to enter.
Philosophy lectures have filled the need for public assembly, and it is not unusual for gatherings to last for long hours. There are numerous state-maintained auditoriums that can be rented out by different groups, and popular ones are sometimes booked years in advance. Science lectures given by the Alchemist Guild have become popular in recent years.
1 Carella, C.J. (2000). GURPS Imperial Rome. Second Edition. Steven Jackson Games.