“I feel like I’m still missing a ‘dimension’ of what you are saying, the part about the ideological differences. How does this frame into the physician/chef example?”
The ideological difference thing doesn’t factor into Plato’s example, because he thought of things like ideology as so many distorted visions of the Form of Justice, that through trial and error, and rational deliberation would be resolved. So, ideology, and its seeming irresolvable difference, is just a “surface effect”.
The counter to this, and you’ll need to see Nietzsche for that, is to point out that this non-ideology of singular truth is actually the Ideology par excellence. Truth is not a thing to be discovered, but a site fought over by different forces. This brings ideology and culture back to the forefront.
This can be done by pointing out that the tools are not ambivalent — when you posit reason and its singularity as depicting the Truth of things, you place value within reason and it’s kind of truth (universal, numerical etc). That requires a further justification, and another, and another … . Nietzsche diagnosed this will to “truth” (singular) as being rooted in the monotheistic instinct, a kind of exclusionary violence. He, instead, thought of truth as an effect of the interrelation and struggles over power between different forces — a polytheistic vision.