It's an interesting dichotomy.

Note, though, that religion only has a unifying effect insofar as competing religions aren't tolerated - or insofar as people willingly convert to it.

My current thought on all this is that we need a unifying religion (which might more aptly be called a philosophy or belief system) whose claims are intuitive enough that virtually everyone could come around to believing them eventually (like in a generation or two).

Here's a post where I've taken a crack at what such a religion / philosophy / belief system might look like: https://nebulasaurus.medium.com/will-humans-ever-settle-on-one-religion-4e50c81b1d96