It's important to recognise that the monotheistic religions, such as Christianity & Islam have a very different view of religion and it's place in society compared to the average polytheistic traditional religions. That difference of views comes in two respects; monotheism carries and implicit true-vs-false religious dichotomy, and second a tendency to universalise - hence Christianity asserted itself as the one true faith for all people.

No polytheistic religion behaved in that way, the Romans adopted and adapted foreign gods and cults into both the fringes and mainstream society, notably the prevalence of the Mithraic cult in the legions and the temple to Isis locate in Rome. So the worship of foreign gods and participation in there cults was not in itself contrary to Roman or polytheistic religions in general - worshipping Isis alongside the state Gods was not a "heresy".

The only real exception being the Cults of Cybele (since priest self-castrate that resulted in a loss of roman citizenship) and Bacchus (owning to causing some amount of disorder). While certain cult practices caused tension within Roman civil law, the Gods of those cults themselves were not denounce or declared false. Likewise the ancient Greeks never declared the Egyptian Gods false.

Additionally joining a cult was a personal choice, an optional extra on top of the state or traditional religion - that traditional religion was part and parcel of being a Roman, or Greek much the same as speaking latin or greek was just part of the cultural identity.

The innovation of Christianity was to separate religion from culture, and to encourage conversion - something that the traditional polytheistic religions did not engage (and modern polytheism such as Shinto still don't proselytise in this manner). Moreover Christianity actively denounced the polytheistic religions as false, polemics and apologetics were never required by polytheistic religions before this still so while Greek philosophy was quite advanced by the time Christianity began to spread it was not utilised to prove religious convictions such as polytheism which were taken at face value.

In this way Christianity spread in the first and second century without much resistance besides persecution by Roman officials, for denouncing the state Gods - such martyrdom did little to detract from Christianity's appeal to the disenfranchised member of roman society. Relatively few scholars at the time took Christianity to be a serious threat, so we see very little by way of pagan responses.

The most compelling cases against early Christians were made by Celsus, Plotinus, Porphyry and Emperor Julian, all member of the (neo)platonic philosophical school of thought. Celsus, On the True Doctrine criticises many aspects of Christianity which modern atheists will be familiar with such as the doctrine of Creation, the central place of man in the universe "why should the world be for man and not for the ant and the trees", and the "absolutely disgusting" doctrine of eternal damnation.

The reply from Plotinus in Against the Gnostics is a more advanced academic lecture, while his student Porphyry's reply was consider so damaging (after multiple apologists wrote extensive responses) his work along with Julians was burnt by imperial edict, twice. Porphyry's Adversus Christianos seems to have criticised the textual evidence for Christianity for instance he "alleged that Daniel did not foretell the future so much as he related the past", while Julian criticised among other things the Christian departure from Jewish teachings (circumcision etc).

But these polemics were not successful in pushing back against the growth of Christian popularity. Ultimately when Constantine made Christianity the state religion of the Roman empire there may have been as few as 20% population of Christians - from that point on polytheistic pagan religions throughout the empire were persecuted.

The only systematic push back came from the Neoplatonic academies located in Alexandria and Athens, with the Athenian Academy being closed in 530AD - seven pagan heads of the school were forced to flee to the Sassanian empire. By this point polytheism was effectively stamped out in the mediterranean, although missions to convert Laodamia (Sparta) continue until about 800AD.

Between the Christianization of the roman empire and the fall of Rome, top down conversion took place - leaders and kings associated with Rome converted to Christianity either to avoid war or political gain, such conversions filtered down society over many generations.

Polytheistic religion remains in the north of Europe, such as Scandinavia, Latvia etc. may centuries after the conversion of the former roman empire - for this reason the Church sanctioned the "Northern Crusades".

As to what the last polytheistic culture standing was there are several contenders, although the question of whether they stopped or just dwindled into the background of history is debatable. The Aztec empire was still around considerably late, and some aspect persist in the Nahua peoples. Shinto and Chinese folk religion are both polytheistic in some sense and practiced today. Some sect of Hinduism and Buddhism are also polytheistic. Within Europe some polytheist practices and beliefs remain among the Uralic and Sami peoples.

Ultimately polytheism never completely died away, but it was forced out of western society over the course of many centuries - over that time while it's philosophy, primarily from the Greeks and Romans has been, absorbed by monotheists (to the point some argue Plato was a monotheist) the very idea of polytheism is made to look foolish and primitive, such as those who insist monotheism was an evolution and the philosophers only endorse polytheism as a concession to public opinion.

I’m curious as to what the last large polytheistic civilization was and what/who they worshipped

To give a semi-definitive answer to your question I would say Hinduism, Chinese folk religion and Shinto are the three largest still practiced "polytheism" in an easily identifiable culture.