>This is where countries with some sort of mandatory service may have us beat.

I doubt it. Turkey has it yet there are plenty of problems between religious people and secular people, as well as between Kurds and other Turks.

The book Influence by Cialdini dives deep into some of the elements needed. Some takeaways that I remember:

Forcing people to be together in unpleasant circumstances, without a common goal they can work towards, does not reduce the us vs them mindset. His example was school, but anything "mandatory" would qualify.

If people are forced to be together, and they work together voluntarily to solve a problem (e.g. by one side needing the other side's skills), then you have reduced polarization.