Were the founders of Roman mythology already believers in the Greek pantheon? Was it an offshoot that developed gradually - both linguistically and mythologically? Or was it a rapid change for cultural or colonial reasons?
Roman culture was not a dry sponge waiting for Greek myth, ritual, and beliefs to fill the void. The Romans inherited an Indo-European pantheon, which paralleled that of the Greeks. At the same time, Roman (and Greek) myths, ritual, and beliefs were no doubt affected by a local non-Indo-European substrata. As was the case elsewhere, there were many changes over time that made Roman traditions distinct. Nevertheless, when they encountered the pantheons of other Europeans, many things seemed familiar. Romans usually attempted to fit the familiar gods of foreigners into their Roman counterparts, taking them to be local manifestations of their own supernatural beings.
Greek myths occupied a distinct place in the Roman perception of myth and religion. Because the Greeks had such a rich literary tradition and they had gods that were easily recognizable as counterparts of the Roman tradition, Roman's embraced that literature, but they did not "just copy the Greek mythology" as is often stated. Romans had their own traditions, which they freely augmented with literature that seemed to enhance their own beliefs. Romans wrote their own literature, sometimes in reaction to Greek writings, but Roman literature took on its own form, reflecting subtle differences in perception.
Unfortunately, much of what we know of Roman religion, traditions, stories, and ritual comes from Roman writings. This gives us a narrow view of what was really going on. We must also understand that Greek and Roman literature was written over many centuries. Traditions change, and we cannot view either as monolithic over time. Literature affected the process, sometimes slowing change, but as foreign influences were “digested,” change could accelerate.
At the same time, the vast majority of Roman citizens were not engaged with the literature of the time. They carried on their ritual practices and told their stories, immune to the direct effect of what anyone was writing – or what had been written, by Greeks or Romans. This “invisible” aspect of Roman religion can be addressed archaeologically and through hints in writing, but it is much more difficult to address. We can imagine, however, that this substrata of tradition was much less influenced by anything imported by the Greeks. The turbulence of waves and tides had little affect on those who lived at greater depths, but unfortunately, we can do little more than imagine what was going on at that level.