Great question. Here's what I think...
It's a lot easier on the personal level than at the societal level.
The big hurdle for society to leap over is the profit to made off of promoting division by reinforcing people's fears. The leaches that sell fear based hate and political division have a constitutional right to spew and there's not a lot we can do to change that, nor should we try.
We can, however, influence people's desire to seek it out by using targeted media campaigns to counter the divisive messages they produce with those that invite cooperation.
The hurdle to do that effectively is the cost of the effort. "We" don't own a big media outlet, or have the budget to produce quality content and distribute it. To be fair, this is being done to the extent it can be with current resources available to those who are working on it, but not in a focused way. There are media sources that do work on producing unbiased content but not really unity by looking for and exposing common ground.
Since before the elections last year, on a personal level, when I have interacted with either "Liberals" or "Conservatives" I have purposely tried to find and expose common ground and there's actually a lot there.
As an example, when I talked to Trump voters about "the wall" it was easy to find common ground by pointing out the expense and ineffectiveness of a wall in comparison to enforcing existing regulations and reducing incentives for illegal immigration, and for making legal immigration easier for seasonal and temporary workers, which all my "liberal" friends would support.
When I pointed out that "Big Corporations" have an obligation to help maintain and improve the communities they sell their products in they agree with that. We all agreed that government waste is out of control and needs to be reeled in.
So, there is common ground and a lot of it, but no money and little effort is being spent on cultivating it.