>300 years ago, the number of religions and ethnicities currently existing in US or Western Europe would have meant a constant state of civil war.

300 years ago the Ottoman Empire was in full swing and quite religiously and ethnically diverse (probably more so than modern Europe or America). Not to say everyone had equal rights or was nice to each other, but historically a cornerstone for the success of many (not all) empires has been a significant degree of diversity and tolerance of both religions and ethnicity. It also wasn't new, Rome was also quite diverse and tolerant. (not always, not to everyone, but still quite so)

That's not true. Look at India - it has many times more ethnicities, and many Indian kingdoms used to have good relations even between Hindus and Muslims before modern times. Also, empires like the Ottoman empire had Turks, Arabs, Greeks, Persians, Jews and many other nationalities; and Muslims, Christians, Zoroastrians and other religions living in relative harmony - certainly not in a constant state of civil war.

Ancient empires were even more diverse, with civil wars often arising more along economic lines than ethnic or religious ones.

And before monotheism took over... well polytheistic societies don't really have "a religion" that is separate from other polytheistic religions. There are lots of gods and people focus on different ones. The next town over seems to have similar gods, but some of the stories are a little different and one or two has a different name... or is that a different god altogether. That town really far away talks funny, every god has a different name and some of them have wildly different stories, but a lot of it is still recognizable...

In other words, religious tolerance with polytheistic societies looks a lot different than the "my god/prophet vs. yours" which is much more prominent with monotheistic religions.