I think we need to be cautious in taking the beliefs of elite intellectuals like Ovid as being representative of the whole society.
Christians always like to promote the idea that the Graeco-Roman gods were ‘silly’ and ‘nobody believed in them anyway’, but this is also a one-sided point of view.
Probably the closest we have to the the ancient religions in the world today is in India, as was pointed out above. There we find a similar situation, with many gods, many shades of belief, many ritual practices, and a mass of of ordinary people who most certainly believe in the gods literally, even in the 21st century.
There are plenty of pre-Christian writers who give accounts of divination, omens, appearances of deities in dreams, miraculous cures, etc., etc. There is the undeniable fact of large numbers of thriving temples, regular sacrifices and offerings, paintings and statues of deities everywhere, inscriptions honouring the gods. There’s no doubt that most people really believed in them, as in India today.
The mystery cults later became more popular, but existed side by side with the established religions.
When the Roman world was Christianized, Christianity was Romanized in the selfsame process, to an extent that I think many Christians are reluctant to admit. It’s natural that this would happen. It’s not for nothing that the head of the Catholic Church is called the Pontifex, the same title as the head of the Roman religion. The robes, the incense, the altars in churches, the processions of statues through the streets on festivals (that you can still see in Italy today), were all taken over from the Roman religion.
Take a look at this scene from Franco Zeffirelli’s 1982 movie of the opera Cavalleria Rusticana. It’s set in a Sicilian village in the 19th century, and has a famous scene with an Easter parade. This was filmed in the town of Vizzini, Sicily. All the trappings of the real Easter parade in Vizzini were used, only some 19th century costumes were added.
Pagan festivals in Roman times must have been very similar indeed. Swap the statues of Jesus and Mary for statues of Jupiter and Juno, swap the one of Jesus with a sunburst and halo for Apollo with a sunburst and halo, make some minor changes to the costumes, and I have a feeling that a Sicilian of the first century BC would feel right at home.
See what you think. Watch to about 27:00