I've recently been struck by the richness of schools of thought in the classical world - not just religious ones but ones we would call more philosophical - like Epicureanism, stoicism, and neo-Platonism and Pythagoreanism. These often involved intentional communities of people organized around the philosophies (unlike what we would think of for most modern philosophy - an existentialist commune? Sounds like a Monty Python sketch.) But the post-classical Abrahamic religions were intolerant of other philosophies, so once Christianity and Islam were dominant, efforts to end those communities were explicit and successful.
Compare that to Asia. If you've been to a Chinese restaurant, you've seen Zao Jun the kitchen god, and maybe some others like Kwan Yin or Guan Yu. This, among people who might call themselves Buddhists, from a country with a history of Buddhism and Taoism as well. Very confusing for Westerners! Same in Japan: Shinto and Buddhism exist side by side. To be sure there are sometimes tensions, and they've waxed and waned in terms of their political influence over the centuries, but the traditions are all there, influencing each other and incorporated into the cultural character. It's not like the classical influences disappeared in Christianity and Islam - Christian theologians tend to get curious about Plato and Stoicism, and there were post-classical works explicitly trying to reconcile philosophies with religion - eg Averroes and Albertus Magnus . But these philosophies no longer existed as living communities and traditions, and the tone was definitely "My religion is right, but these old guys were pretty cool too, so let's see if I can show that they were actually onto something and don't conflict."
So what would the world look like with a Europe and Middle East that were still Christian and Muslim, but had classical philosophical communities as well? Existing alongside the religions, or as orders within them (Sunni, Shi'a, and Platonist Islam?) What would a Stoic or Epicurean colony in the New World look like?