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)