I think it is within the realm of possibility that a human could, as whonunuwho said, train themselves to be a robot and look at things completely objectively, but a person would be working against nature, I think.
On the other hand, I do think it is possible for people to think about things they don't particularly care about objectively. For example, I'm a Phantom Of The Opera nut, so I tend to judge Phantom related stuff really harshly. If I love it, I love it. If I hate it, someone gets hurt. But that's because I have an emotional attachment to it. I'm invested in it. But take, say, Sherlock Holmes. I understand that the original stories are very well written and clever, but I'm not so crazy over it that I can't look at the recent movies and enjoy them for what they are, even though my hard core Holmes fan friends got a rash from them. If any of that makes any sense.
But I also think the question is moot from an intellectual stand point, as we need to have different opinions and views of things in order to see a thing fully. Even being completely objective, one person can't see all sides of a situation at any given time. We need other people of other opinions to point things out to us for fuller understanding.