However, I see people's personalities informing how they behave in their occupation all day, every day. The notion you can subconsciously remove all of your biases before undertaking a project is, surely, inherently flawed?
We also deal with associations - the body of your work will be judged based on its context. Its context comes from who you are, what you believe, and your values (both work and personal based). Of course an artists' work will be looked at differently if they're a UFO believer or not. Of course people will question whether someone championing an inclusive organisation can really not support gay marriage. Of course people will look at the works of Roman Polanski through a different lens because of allegations. It's not enforced "political correctness" it's default behaviour of humans to make these links, correct or not.
Personally, I'm tired of the "leave politics to your political circles" response - politics has an impact on your worldview and thus influences your work.
I'm not claiming everyone should hold the same views, but the expectation that people with diametrically opposed outlooks on the world should "just get along" for the sake of a project seems absurd to me. It's why most companies have values, and is pretty much the only non-BS use of "company culture".