Explanation: In pre-modern polytheist faiths in general, but Hellenic religion in particular, there is a tendency to adopt the gods of one's neighbors - or rationalize them as the same god under different names. To the Romans this was the Interpretatio Graeca/Interpretatio Romana, depending on what time and cultures you're discussing. To the Romans, the gods were the same all around the world, just worshipped and seen differently. This made it very easy for Romans to spread their own practices and to adopt the practices of other faiths - Roman gods usually had many epithets representing their varying aspects (MARS SILVANVS for Mars as god of the woods, for example), so to tack on a provincial name was no problem at all - MARS LENVS was both Lenus, Gallic god of war, and Mars, Roman god of war; the Romans saw no contradiction in it.
Furthermore, to the Hellenic faith of the tradition practiced by the Greeks and Romans, correct belief ('orthodoxy') was of secondary importance - correct ACTION ('orthopraxy') was what was vital. Usually envisioned as 'paying the proper respects to the gods' rather than a united moral code.
On one hand, this is a very tolerant outlook, and that is commendable. On the other hand, it could lead to some curious ideas about other faiths - ranging from the eccentric (equating Wodan to Mercury because they're both traveling gods) to the outright offensive (asserting that the God of the Jews, YHWH, was just IVPITER CAELVS, Jupiter as envisioned as the sky itself, since the Jews didn't and don't make idols of their God).
Not particularly - the Romans sometimes adopted 'cult' gods (such as the Egyptian goddess Isis, or the Persian god Mithras) which were worshipped separately, but even those were sometimes conflated with traditional gods. There's even evidence for interpretatio Graeca as far east as India!
Note that one of the reasons the Romans were so good at this interpretatio was because they weren't very concerned with getting the details right - as mentioned, Wodan (early Germanic equivalent of Odin, king of the gods) was equated to Mercury (god of trade and travel) because they both traveled. That's... that's REALLY trying to fit a square peg in a round hole. And even the monotheism of the Jews was rationalized as just "worshipping Jupiter, but only Jupiter, and as the literal sky", which is... also quite a leap.
But, in a sense, they didn't need to get the details right - the provincials would worship their gods in (what they saw) the correct and traditional way, and the Romans would continue to worship that same god in their own way. It was more of a way of looking at the world than a strict theology.
Real talk: this is exciting and awesome information that I hadn’t considered that I didn’t know. Especially your first comment about matching up gods. Unsarcastic wow.
It makes you wonder about the Carthagenians and Druids. Both religions the Romans persecuted heavily. Makes you wonder if the accusations of child sacrifice and ritualistic cannablisim was ancient propaganda or if there was some truth in it. Cause they were pretty tolerant* to just about everyone else.
*Tolerant by ancient conquering slave owning rampaging army standards.
I might be able to offer some insight here - Carthage, as a state, was unduly burdened and then eradicated in a, quite frankly, shameful manner, but Carthaginians were ethnic Punics. Rome, after Carthage itself was destroyed, allowed the Punics of North Africa to continue practicing their culture, religion, and language without interference. Hell, in the future, Emperor Septimius Severus was part Punic, even, and spoke Latin with a Punic accent! So it's really just a matter of the Roman Republic holding an irrational grudge against a single city.
As for the druids, they were wiped out, specifically, because Rome was trying to keep the Gauls and Britons from revolting as much as they could. Druids were a priestly caste, but also a caste of leaders that people could rally around. Other Gallic and Briton religious practices survived unmolested.
Both were also accused of human sacrifice by the Romans (who considered such practices both immoral and an offense to the gods), and whether that was true is a whole can of worms waiting to be opened. "Not today, Satan" I say!