Objectivity and truth become not simply unattainable goals; they cease to exist as meaningful concepts. This is post-modernism run amuck, and it reveals a void at the core of a large strain of multicultural academic work that is much larger than simply removing the word "science" from a mission statement may suggest.When religious true believers take over school boards and install creation science in their curriculum, they are operating from a coherent, if wrong, belief system. When cultural-studies types take over anthropology departments and remove science on the grounds that it's a social construct, possibly a gendered rape manual, they have lost the good of the intellect in an assault on coherent beliefs of any kind, the end product being an academic culture in which a university that operates as a subprime party school is no less useful than a university that insists on coherent thought.
LOSING THE GOOD OF THE INTELLECT. John Rosenberg suggests it can happen to an entire discipline. See his Rigoberta's Revenge: The Implosion Of Anthropology. It's a long essay, with extensive quotation and citation of other essays, and those will reward careful study. Professor Rosenberg concludes with what I hope will be the epitaph for cultural studies' attempt to hijack higher education.