I'm looking always to learn, not to paint you into a corner where you need to concede that I or anyone else is right. With that front and center, where I keep struggling with what you say is that it seems to contain a straight contradiction.
On one hand, you say that some things can be decided with a die roll and that's all fine. In those cases, it seems like the PC/NPC involved was satisfactorily reduced to a die roll. On the other hand, you say that PCs/NPCs can't be reduced to die rolls. That seems like it is in contradiction.
It's like saying - Alice is allowed to impact what you do with the number she assigned to her Strength, but not with the number she assigned to her Charisma. Say Barbie decides to make Alice stop helping the villagers by grappling her with Athletics. Now, I think characters shouldn't use hostile effects on one another at all, but not all groups play that way. So if we are in a group where it's okay to do it, are you fine with Barbie imposing her will on Alice with Athletics, but not with Alice imposing her will on Barbie with Persuasion? That's the part I don't follow.
I don't see the contradiction. Physical activities can be resolved with die rolls. What someone is thinking can be influenced by, but not resolved by, die rolls unless magic is involved. End of story.
By dictating what the barbarian thinks, you have effectively stated that the barbarian doesn't belong to the player running the character. Instead the PC really belongs to you. Or to paraphrase an old meme as a DM you are saying "All character are belong to me".
So here is a question for you guys who disagree with my view.
If you were DMing a game that allowed interparty conflict and one character built a pure combat oriented character and the other built a social character and the combat character got it into his head to attack the social one and the social one was trying to persuade him not to kill him.
How would you DM this? You would let the combat character use all of his abilities on the social one and disallow the social one from using his to defend himself?
The social one can try to convince NPCs to come to their aid. But they can't control the thoughts of the attacking PC without magic. If, for example, they do a deception check, the only thing you can tell the attacker is that the social character is sincere. What happens next is up to the players.
Don't want that to happen? Don't allow PVP.