There is a space between when a character has a consistent characterization and when the author loses the power to change the characterization. I used Batman as an imperfect example of a character who exists beyond the control of a single author (partially because the cultural image makes it resilient to changes) but Dun is a character that still remains under the control of a single author. Although this is a continuum.
In that space something is lost if the players' interests come in conflict with the character acting in character. However I would argue the players' interest come first. And I think your school of thought would agree, although I will need to elaborate.
The school of thought you were trained in has one of the foundational player interests be consistent characterization. So when a character's characterization comes in conflict with other player interests, it is also coming into conflict with this foundational player interest your school of thought has. I don't conclude the character must change. I conclude you should address the conflict of player interests.
From there, the rest of your post seems like one of multiple valid outcomes of addressing that conflict of player interests.
Personally I too highly value character consistency as one of my values, this is why my consistent answer through this thread was "ignore the excuse that hides the player's interests, talk about the harder topic OOC" rather than a concrete always X or always Y.
Sometimes multiple players contribute to the same conflict. The DM and the player controlling the PC can both bear some responsibility.
As always I suggest dealing with conflicts of player interests OOC.