Choosing to to be apolitical is a political stance. It would be nice if we could magically divorce people's work from their stance, but their stance will affect how they treat their peers and juniors- this is how patterns of oppression become systems. If a person has beliefs that women are inherently less capable of work, they will be unlikely to volunteer women for promotions or even see their women coworkers as having performed the work done. If a person has beliefs that black people are more violent or thuggish, they are unlikely to view that black coworker asserting that a technology requirement is utterly stupid in the same light as a white coworker asserting the same.
I should emphasize these are not conscious, malicious behaviors. We are taught things about our peers and these teachings change our views on the context of the work of our peers. People rarely consciously, maliciously try to prevent the advancement of a disenfranchised group. Instead, their beliefs of that group prevent them from seeing that a member of the group deserves advancement.
People do not differentiate from the contexts of their pervasive views on how they view every other person around them. They do not cease being sexist because their workplace claims to be apolitical. It merely means they no longer have repercussions within their workplace for their beliefs, regardless of the countless absolutely unprovable ways these beliefs bleed into work.