All across the Empire, massive church buildings were erected by emperors. Right from the beginning of “official” Christianity, Constantine financed construction of huge churches, including the Basilica of St. Peter in what is today the Vatican (at the time it was an obscure graveyard in Rome). The traditional Roman public buildings, including forums, theaters, bathhouses and so on, were often neglected in favor of churches, and many temples to Roman gods and other public buildings were repurposed as churches.
Once it enjoyed the support of the Roman elite, the Christian church began incorporating non-Christian holidays into its own liturgical calendar. December 25 had been the major festival of the sun god Sol Invictus, and early Christians embraced the overlap between that celebration and Christmas, noting that Christ was like the sun as a source of spiritual life. Other Christian holidays like Easter coincided with various fertility festivals that took place in early spring, around the time of the spring equinox. The tradition of saint's days, holidays celebrated in veneration of specific saints, often overlapped with various non-Christian celebrations. Most church leaders saw no theological problem with this practice, arguing that the ultimate goal was the salvation of souls through conversion, so it made perfect sense to use existing holy days and rituals in order to ease the transition for new converts.
That being noted, the incorporation of non-Christian celebrations into the liturgical calendar did not imply that Christians were willing to accept polytheism. Unlike most ancient faiths, Christians could not tolerate the worship of other gods, which they regarded as nothing more than nonexistent delusions that endangered souls. They used the term “pagan,” coming from the Latin paganus, which means "country bumpkin" or "redneck," to describe all worshipers of all other gods, even gods that had been worshiped for thousands of years at that point. The point here is that Christians used scorn and contempt to vilify worshipers of other gods - "pagan" indicated that the non-Christian was both ignorant and foolish, even if he or she was a member of the Roman elite.
It took about a century for the believers in the old Roman gods, especially the conservative aristocracy of Rome, to give up the fight. As money shifted toward building Christian churches and away from temples, so did Christians sometimes lead attacks to desecrate the sites of pagan worship. Riots occasionally broke out as Christian mobs attacked worshipers of other gods, all with the tacit support of the emperors. In 380 CE the Empire was officially declared to be Christian by the emperor Theodosius I and all people of importance had to be, at least nominally, Christians. There was no sustained resistance to Christianity simply because “polytheism” or “paganism” was never a unified system, and it was impossible for people who worshiped a whole range of gods to come together “against” Christianity, especially when it was the official religion of the Empire itself.
A much more difficult battle, one that it some ways was never really won, had to do with “pagan” practices. Everyone in the ancient world, Christians among them, believed in the existence of what is now thought of as “magic” and “spirits.” Christian leaders came to believe that, in general, magic was dangerous, generated by the meddling of the devil, and that the spirits found in nature were almost certainly demons in disguise. There was very little they could do, however, to overturn the entire worldview of their followers, considering that even Christian leaders themselves very much believed that spirits and magic were present in the world, demonic or not. Thus, pagan practices like blessing someone after they sneezed (to keep out an invading spirit or demon), throwing salt over one's shoulder to ward off the devil, and employing all manner of charms to increase luck were to survive to the present.