So you've been waiting for five hours and nobody more qualified responded so I'll give it a shot. The Roman Pantheon existed long before the conquest of Greece. The Greeks had colonies all around the Mediterranean including Magna Graecia in Italy and probably influenced Italian religion at this time.

The Romans were pretty tolerant when it came to religion and often adopted foreign gods into their ever growing pantheon. From what I understand Rome left the Greek religion alone, in fact Hadrian made a point to visit Greece and take part in their rituals.

Getting a religion banned in Rome was really hard because religion was decentralized at the time and that in a polytheistic society it was really easy to just add anything to the pantheon to make it legit. In fact many secretive cults flourished in the empire and were tolerated (I believe the Cult of Isis was a favorite).

Besides Christianity the only backlash I could think of against a religion was against the Syrian God Elagabalus (also known as Heliogabalus and later as Sol Invictus). But this was more against Emperor Elagabalus pushing his religion on Rome and defacing established temples. But even then Sol Invictus later became very popular in no small part due to Emperor Aurelian.

But as you're probably aware Christianity did get persecuted pretty badly but it was a special case. The story goes that Emperor Diocletian was trying to get his fortune told but the communication with the Gods kept getting interfered by a Christian servant praying to himself in another room, which was taken as a sign as Christianity putting a rift between Rome and their gods. That combined with Christians having an empire spanning network with an established hierarchy and it didn't take long for conspiracy theories to follow.

But the mileage of Diocletian's persecution varied because at the time there were four emperors and not all of them were keen on killing seemingly harmless Christians.

Hi, Classicist here.

The Romans adopting Greek gods etc was part of a widespread Eastern Mediterranean practice going back to the bronze age, one of syncretion and assimilation. Thus Greek Herakles is often associated with the Tyrian Melqart, Zeus with Ba'al Haddad and so on. The Romans, like the Etruscans just partook in the same process.

Note that as /u/The_Magic says the Roman pantheon existed long before Greek contact (and many aspects sprung from a common source). Moreover one has to differentiate between writing about the gods and mythology and actual practice. The Roman major cults remained remarkably conservative throughout time and Greek influence there is minimal to non existent as one can see from a hoard of inscriptions and historical writings. This is something people often fail to do.

As for Greeks worshipping their gods well by the time the Romans arrived on the scene things have got fuzzy. From the successors onwards Greek cults are starting to change under foreign influence, both Macedonian and otherwise, and so the direct civic equivalences one finds in the classical age soon to cease to exist. Modes of worship change too. The system is now more generalised (so one might now simply worship "Zeus" rather than, say, "Zeus Melikhios" as a specific Attic deity etc) and therefore quite receptive to new ideas.

Over time we ascertain a merger and a separate Greek identity ceases to exist, they simply become Romans and remain so for centuries. So if you're after later Greek religion then you have to go to books focusing on late Rome, the second sophistic and so on.

As for getting a religion banned you have to be a group of dickheads basically.