The way romans are usually represented compared to other cultures in pop culture, they never show devotion to religion. In viking movies and tv shows you see devotion to Odin and the gods, in medieval movies devotion to Christ, but in ancient Roman movies, they are shown as people living morally gray apathetic lives without piety or deep care for religion. They are almost inhuman, completely unrelatable. This always seems strange to me. Did they take religion seriously? Was it comparable in intensity to the way religions like Christianity and Islam are treated? Was there punishment for blasphemy like other cultures? How passionate were they for their beliefs and gods?
Pop culture really does the Romans wrong when it comes to their religious beliefs.
As a matter of facts Romans were very religious, Pompei shows the Romans had private altars celebrating their ancestors as divine protectors of their homes called "Dei Mani" while from their military campaigns we know the Romans practised estensevely many rituals to gain the favors of the Gods, many authors such as Cicero reference the gods as the moral standard which a true should follow, the "pax deorum" also gives us a huge insight on the religiosity the Romans had.
Romans celebrated many indigenous gods such as Caco (later Vesta), Mars and Quirino and following the indo European migration in the Italian peninsula many Indo European gods were also introduced such as Jupiter, Hercules and so on (these gods were essentially already worshiped by the Romans long before the Latins came in contact with Greeks).
Romans were very politheistic in nature, single gods had numerous aspects to them an example might be "Iove Pluvius" who was the "rain aspect" of Jupiter, and each of them were celebrated in diverse rituals, Roman legionaries would carry little clay or wooden statues of their favourite gods and pray to them in their tents.
Overall it can be stated with certainty that Romans were very religious despite what Hollywood would let you believe.
I hope you will get a response from one of our users soon, but as you are waiting you can read some earlier posts related to this subject. To summarise, it seems that even though the myths were often questioned, religious rituals were taken seriously and were definitely seen as important.
In this answer, u/UndercoverClassicist discusses how the Roman religion focused more on right practice than right belief (really the entire thread is worth reading but the second subheading in the highlighted post gives a basic rundown on the issue). On the same subject there is furthermore this thread by u/AndrewSshi which also explains how foreign deities were integrated into the religion and an answer here by u/randomasiandude22 with a focus on the Roman military. For more specific examples, you can read this older discussion by u/mp96 with examples about how Roman sacrifice was done, and in this thread u/bigfridge224 writes about the strange and cumbersome taboos that surrounded the High Priest of Jupiter.