It's worth considering what changed. Demographics changed, but we've always had some kind of mixed cultures and ethnicities. The history of it has been an expansion of who gets to be the "majority". Like Rome redefining who is a citizen.
Maybe it's broadcast media, but there's been national publications since the founding of the US.
Looking back to Antiquity, our situation doesn't seem so abnormal. I think it's just the ebb and flow of how groups of people interact with each other.
- Who counts as a citizen
- Who has the land
- Who gets welfare/benefits
- Who is anathema
- Who mediates power (bureaucrats? nobility? monarch? people?)
It's like a laundry list of issues that bagged ancient Rome, enlightenment France and late Tsarist Russia.
EDIT: It blew my mind when I actually started to read up on the French Revolution and found that besides what to do with the Monarchy, the issue that really divided them was Universal Manhood Suffrage. For years I had been fed the vague notion that some quasi-social-utopian issues were at the heart of it. But they really just couldn't agree on whether all men should be allowed to vote.
- Me, not all that many years ago
- law enforcement
- public transit
- property taxes
- building permits (i.e. regulation)
- zoning
- public employee pay/benefits
All redound to these basic beliefs and have the added problem of affecting people personally too.
The key, as you pointed out, as did Buttigieg, is to identify areas where there are shared problems you can work together to solve. There's something about local government that seems to encourage this, in my opinion. Maybe you think gay people are awful and I go the pride march every year. Guess what, the water main is still leaking, and building permits take too long. Maybe we can just focus on working together to solve real problems, and accept that there are a range of social issues where we probably won't ever agree? And that's just fine?
I think we used to know how to do this in the United States, but something changed.