It still won't fix the problem. The fact that you can talk to any NPC in the game with every character in your party but the game will treat everyone exactly the same.
Unfortunately, no. Several of the dialogs are one-offs and cause approval/disapproval from other characters. If the MC isn't the one in the dialog, they do not get the option to cause the approval/disapproval. This bug has real effects on relationship mechanics.
Does each (Origin) companion have approval for other companions? That'd be an interesting mechanic, and more in line with Larian wanting all companions to be ~main characters.
I.e., if you respond as Tav, then origin companions' approval of Tav changes. But if you respond as Lae'zel/etc, then every origin companion's approval of Lae'zel changes. To make it work better in multiplayer, I suppose only characters who aren't currently being directly controlled by a player would have their approval change...
Related question: am I remembering correctly that currently, if I have two custom characters and 2 Origin NPCs, each Origin NPC has a separate approval for each custom character? It's been a while since I played multiplayer...but if so, then this means that the mechanic for character-specific approval is already in the game.