To put it as simply as possible, a meaningful consequence is something that changes the status quo in a way affects play going forward.
In other words, a change is meaningful if the player has a reason to be invested in it. Is that fair? For example, if my character's cloak randomly changes from red to green, it only matters if I as the player feel attached to that cloak or think my character is attacked to that cloak, and either I or my character don't like green. I think we would agree that although the change of the cloak from red to green changes the status quo, it doesn't meaningfully impact the way play goes forward if I don't care about the color for some reason.
To me, that includes change that is entirely character motivated and driven, and does not inherently require a mechanism of enforcement.
Agreed. For example, I offered up the sort of ideas you are now going to elaborate on already:
Getting kicked out of a faction. Having a town's opinion of you go from friendly to neutral, or neutral to reviled. Losing precious time. Your foes escape...
I to have seen these sorts of things taken to heart by players and have a visible effect on future actions. And that's great. It's always wonderful when the player is emotionally invested in the imaginary world that we've created together. I love it when players become emotionally attached to an NPC, because that changes there play in a meaningful way - just as you suggest here - and it validates that I've created a pretty cool NPC.
But the thing is, all of that is like the forced march through the wilderness when there are no mechanical consequences to fatigue, heat exposure, starvation, or thirst. Sure, you could have a player so invested in the experience that they roll play out the hardship all on their own, adjusting play to account for how they think their character would feel under the circumstances. You wouldn't even need mechanics for death. They could just say, "You know, after 5 days of this blistering heat without fresh water. I think my character would just lay down and die. They couldn't go on. Time to concede and get a new character." Why would we even need mechanics? Why would we even bother to roll the dice? Or conversely, in the same party you could have a different player say, "My character marches on tirelessly without rest for a whole month, neither drinking nor eating - kept alive by their will to live." Again, why would we even need mechanics? Why would we even bother to roll the dice? All that matters is player investment right?
There is nothing that forces a player to "take heart" in any of these things in a standard game of D&D. Kick out of the faction? Who cares? Town's opinion of you goes to reviled. Who cares? Foes escape? Who cares? When your only consequences are left down to the player's choice to invest in them, changes are a good portion of your table is just going to not care. What do you do when 3 of your 5 players only care about leveling up and improving their character? Salient enough to matter to certain tables is not the same thing as salient enough to matter.
The thing is that if you care deeply about whether you are in the faction whether or not you have some mechanical benefit for being in the faction, you probably don't mind that you do. Getting some small in game benefit for being part of the Knights of the Sacred Chalice doesn't harm your valuation of it's just really cool. If you really care about your reputation in the town because you value the opinion of this NPC, it probably doesn't harm you that having a positive reputation has some meaningful in game benefit.
But the reverse is not true. And because the reverse is not true, it's generally not people that "take heart" in all these story elements that are clamoring for mechanical consequences to be removed. There is a very strong correlation between people who don't want consequences and people who don't want to care. There is a very strong correlation between players who don't want consequences and players who don't want to ever not get there way. And in my experience, this gets dysfunctional in a hurry.
But OK, if this is your answer, that some tables are so invested in story elements like the approval of NPCs that this is meaningful and that's the core of the game, why don't make that game? Why have hit points? Let's just have a reputation system? Why have a combat system? Let's just have social approval as the metric that matters in the game. Why not make your relationships to other NPCs have meaningful mechanical effects on play? Plenty of games do that. If that's really the core of game play and not trudging through steaming jungles and fighting monsters, why don't we play a game that facilitates that instead of having an illusionary combat system that produces no negative outcomes. Let's just have a system where if you want to fight something you win, and dispense with the dice rolling under the principle that you shouldn't roll the dice if nothing is at stake? Or maybe we should have a system where you win combats only if you have the approval of important NPCs, and lose them otherwise? That would be interesting.
And I know you are hedging your position in this by saying, "And like I said earlier, I don't exclude death, or other stark consequences." But I can't help but see some self-contradiction in saying that the game should be primarily about the D&D experience of dungeon crawling, adventuring, fighting and so forth but that there is no need for consequences to that, because there are these tangential abstract experiences that a group could potentially become invested in. Yes, but it would seem like D&D is a strange game to focus on then.