First, take the Greeks as an example

The Greeks didn't have a super strict polytheism. Who the Olympians were was a more or less settled question, but there were still plenty of minor deities and daimones (such as the river god of the Iliad), and we know of cults to foreign gods. With this in mind, it was not such a world-changing idea that other gods existed in other lands. When the Greeks then settled in some of these lands, such as Egypt after Alexander, they sometimes adopted or syncretised these gods. As an example, we see the syncretic Amon-Zeus, with both Amon and Zeus being key deities in the two pantheons, it was logical to see them share a spot.

Looking at the Romans, we also see the idea of different lands having their own gods, and that these also needed worship to maintain the Pax Deorum (peace of the gods). This is why Rome had what some have (anachronistically) called a kind of "religious freedom". The logic being that the locals know best how to worship their gods, so if we let them do it, their gods won't cause trouble for us, and the Pax Deorum will be maintained. Rome, too, saw some cults, such as the cults of Isis and Mithras, grow quite popular.

One quite peculiar example can be found with the Norsemen. As the Norse travelled the world, they came more and more into contact with Christianity, and kept hearing of some guy who apparently conquered death. With that, we saw the figure of Hvidekrist show up. It was never a particularly widespread figure, but we do have archaeological finds showing depictions of Christ and jewelry with cross-motifs (my personal favourite of which being a Mjølner with a wolf-head in the rough shape of a cross, and with a smaller cross cut out in the centre).

A common feature of polytheistic religions is also the lack of a strict canon, and with the lack of such, there was little preventing or desuading them from integrating the new gods they came across, as they found them. It's not a question of reconciliation, as that suggests something doesn't add up, but rather a question of how they expanded their spiritual horizons

Edits for typos