the only thing I can think of to do, as an individual, is to build community with people who say "no, there really are not two sides to some issues, and we don't have to embrace the viewpoints of those who disagree on fundamental issues like human rights". also to support news orgs and other media who take a similar stance.
this is unfortunately what (mostly right wingers) decry as "bubbles" and "echo chambers", but I think if the left is going to win hearts, minds, and political power it needs to focus on engaging its own people on its own issues rather than waste time and energy endlessly fighting with the right.
also, inviting conservatives in to find common ground is largely a trap anyway, and has shifted the overton window a good deal to the right because people feel that "okay, maybe we can come to some sort of compromise". the writer a r moxon put it very well: "meet me in the middle, says the unjust man. you take a step towards him, he takes a step back. meet me in the middle, says the unjust man."
on the other hand, I've read that when people complain that their kids went to college and got "brainwashed with liberal ideas", what actually happened was that they met gay people, and black people, etc, and realised that most of what their parents were getting off conservative media was bullshit at best and hate-mongering at worst. so maybe the real solution is to welcome conservatives, but hold the line on making no space for conservative ideas and attitudes.