More and more I think a good answer for this is something along the lines of "...a shared basic reality of facts." Especially lately in the US it seems like there's a schism in the basic understanding of what's happening with stuff like Coronavirus, effects of systematic racism past and present, climate change, etc.
I do not wish to speak for anyone else here, of course, but the concepts of "true" and "false" don't really map on to my physical human dimension of reality very well at all, if I think about it! Observing something as "true" is just observing it. Maybe other peoples' thought patterns run differently? Serious question here for you all, my wonderful fellow HN readers: I don't really walk around in what I perceive as reality thinking "that's false, and that, and that over there too". Exactly the opposite! Everything I observe is true, because I observe it. I don't even think about perceiving reality at all. Everything that Is, just Is. This isn't meant to be coy or cutely condescending — I've legitimately just never thought about thinking very much before now.
My concept of the "necessary-shared-binding-force-between-things", if you will, has thus moved away from constantly bikeshedding "truth" and toward the simple observation that all things that Exist exist and all things that Don't don't, such that when another human describes experiencing our physical dimension of reality in a way different than my own, the fact that they experienced it is what's true, not the thing they're talking about when they describe the experience, since I might still completely disagree with that.
Most people have usually also gone one leap beyond "experiences" just within their own mind or some smaller slice of community before it's possible for me to hear from them, so what they will actually share are their proposed solutions to the problems they experience in reality. These suggestions are at times very distasteful to my particular (not-Truth) set of values, if you know what I mean, but still must be ignored and/or forgiven if I want to hope we live together here on Earth. I don't see any other possible alternative if I fail to scream loudly enough at all 9 billion of us until finally we all agree (with all of my suggestions, of course) and can stop arguing, all at once, forever. No solutions aside from the, uh — you know, distasteful ones.
It's been very personally meaningful to me to be able to find something I can consider "true" in common and makes it a lot easier for myself to communicate with other humans who might hold views I find abhorrent, especially when those are toward groups including myself. My views toward our physical-reality-at-large didn't change at all either — I'm the same typical Bay Area lib-left as ever. I'm not suggesting important and difficult subjects should stop being discussed, be discussed less-intensely or less-frequently, or be discussed among a smaller set of participants. I just feel that discussing them will be a hell of a lot easier once every attempt to do so doesn't begin with an existential punch-in-the-face basically telling the other person that they must be lying about the way they perceive reality.
Thinking about it a little more: isn't it kinda extremely fucking amazing that any "truth" or "falsehood" we short-lived humans throw back and forth at one another was, at some point possibly thousands or even tens of thousands of years ago, toggled from a state of non-existence into a state of Existence by a single human mind? Forgive me for torturing the metaphor a bit too hard, but that's one form of true equality I can believe in: that every human mind has the godlike ability to Create new informational "lifeforms" out of complete nothingness. These days AIs have that ability and are our equals too!
It's pretty cool to think about how the moment any new informational lifeform is shared by its creator with any any other mind (human, artificial, or otherwise) it becomes forever outside of its creator's control. You can't really kill them, but the various humans (and otherwise)[0] comprising my country's Federal government has sent many well-intention humans to die fighting wars that try to. You might be able to slow or even stop the spread, but all it takes is for one other person to find one copy of one old book, and boom, it's back[1]!! This made the Dawkins definition of "meme" make immediate and intuitive sense.
[0] https://www.youtube.com/watch?v=eKl6WjfDqYA
[1] You just lost The Game.