You make the argument that sociology is its own thing that can't be conflated with math which I think every one agrees with, isn't that the premise of the article?
Sociology has its time and place and thats in sociology, just like Math has its own time and place Math.
Mathematical truth and logic is often used as a gold standard for universal truth. And it is then often used as a straw argument to simply push away complex and uncomfortable questions. (A hyperbole of such a misguided line of reasoning would be "Software is just maths/logic and therefore pure and we so don't need to think about sexism and other social issues in sofware engineering.". A more nuanced version would be parts of the article we are discussing.)
But the "default tech" when thinking about mathematical truth (for example predicate logic) is in itself biased towards universally definable truths: A given predicate is universally defined a-priori.
There's no tools for things such as conflicting definitions and speakers positions in predicate logic: In reality, different actors in a discussion might not agree on what even they are talking about.
Take as an example the often discussed statement "White people can not experience racism". If you try to naively approach this with the toolset of universally definable notions you quickly realize that it can not be true (assuming a definition of racism that is not in itself skewed).
But there is a lot of things going on here: Who are these white people? Is the statement "This person is white" even based on a well defined predicate (Hint: It's not)? Etc etc.
And so: If the only logic in your toolset is predicate logic, it's hard to grasp sociological issues.
That said, I'll agree that it sometimes feels like there's two types of people, the ones that think everything is amenable to rigorous and objective reasoning and the ones that think nothing is. But it's important to realise that both these modes of reasoning are important. For example, a mathematical proof can show that there exists no perfect voting system under some reasonable definition of "fairness"[0], but the theorem itself cannot decide whether that definition of fairness is really the one we care about.
But it's one thing to say that "there are more modes of reasoning than ones that lead to objective outcomes" and quite another to say that objective facts play no major role in our society and that getting people to understand that you can't always bend reality to your preconceptions isn't incredibly important.
[0]: https://en.m.wikipedia.org/wiki/Arrow%27s_impossibility_theo...