The statement "objectivity is a tool of white supremacy" is generally used to refer to asserting confidently objective truth exists, which is more of a philosophical statement than a refutation of the scientific method like it's often framed.
The use of perceived objectivity to enforce linear thinking and silence people who react emotionally is why this comes up in the literature you're referring to. You wouldn't tell someone crying at the death of a loved one that crying isn't an objective response to the situation at hand, but this happens in many ways ("why are you so upset about X behavior from a colleague? -> you are behaving irrationally" rather than trying to understand why someone was upset, and knowing everyone reacts to things differently)
This is a topic on science and the example about someone crying over someone's death is a strange example. It's clear that if it wants to be called "science" then it has to have what you call linear (vs circular?) thinking. And yes there is an objective truth as far as what experience can measure.
Saying "everyone reacts to things differently" is a truism. Then what? As everyone reacts differently, the logical result is to IGNORE the emotional/irrational part of people when we deal about science/technology. As simple as that.
I don't read it quite this like. “science” concepts still have emotional impacts on people, especially when many things outside "hard" science get framed as science — think about all the management advice that gets passed around as objective fact (that also changes every few years, oops!).
it's not arguing about the truth of how many electrons are in a carbon atom, it's your boss arguing that they have a "scientifically proven" management philosophy that is objective. would you believe someone if they said that? even if they showed you a study?
It's "hewed", not "hued"