Mark asked a great deal of direct questions in his first post, so I'm going to respond using those questions as a guideline for my thoughts.
How much do your personal politics and philosophy influence your ability to appreciate art?
I believe truly good art should make you question (or at least reflect on) your personal politics and philosophies. I don't really mind if a work of art is trying to make a certain point that I don't necessarily agree with (completely), but if it is so unoriginal, unrefreshing and boring that it doesn't even make me (want to) reflect on my own views, I will not appreciate it at all (on a content level). If an artist tries to tackle politics or philosophy, it should be in a way that makes me ask some really profound questions (preferably questions that I've never asked myself before).
I have to admit that I'll probably be more willing to forgive (for instance) films that do seem to defend worldviews or life visions that I tend to agree with, even if they aren't necessarily that profound or refreshing, but I do think I've become a much more critical person in that respect compared to a couple of years ago.
I also have to point out here that most of my personal convictions have become much more flexible than for instance three years ago, while only a few others have become "firmer". I suspect that the increased flexibility is (in part) a result of my journey through cinema, because it has exposed me to worldviews of thousands of film characters and hundreds of writers and directors. Personal beliefs are always partly a result of your environment and as cinema has been a big part of my environment during the last couple of years, it has changed my ideas about life quite a bit. Art influenced me as a thinking person.
Do you only like movies that reflect your beliefs, or is it possible to separate the art from the politics?
It's not possible to separate them, unless you're (for instance) only interested in judging the technique of a film, while not caring about the substance. I think I'm definitely a person that is able to do that, so in that sense I'm very open-minded. I don't mind watching films that I think are inherently stupid as long as the cinematic aspect of the film is a pleasure to behold and interesting to study.
If you want to consider yourself as someone who speaks with a certain sense of wisdom, I think you're obliged to constantly confront your own ideas, for instance by means of watching films or reading books that go against your established beliefs. So, yes, we should definitely try!
Are you able to appreciate art with hateful subject matter?
Yes, because it can sometimes make me understand how the mind of hateful people works. I may not agree with the intentions behind the art, but it can still inspire new understandings and perspectives of thought. That's always interesting.
For example, The Birth of a Nation and stylish Italian horror films. Is it fair to enjoy one despite its inherent misogyny while decrying the other for its blatant, if equally-ridiculous, racism?
Enjoyment is not a choice, so in that sense it's totally "fair". You enjoy what you enjoy.
If you want to be consistent, you need to be able to substantiate your enjoyment as well, though. So in these cases, I think it would be fair to defend the films for their technique and justify your enjoyment like that, while still pointing out the problems they have content-wise. As I already stated, I think that kind of "separation" is perfectly possible and I do it very frequently.
At what point in your viewing does your opinion on a piece of art or film change? How grievous a sin does the film have to commit? Is it just a star's or director's politics, some violence or subject matter, a star's face or an overall unpleasantness. I realize that what's unpleasant for one is seventh heaven for someone else. But that's part of what I'm getting at.
That's a pretty difficult question. I think you're only talking about content here so I won't say things like "bad editing" and stuff like that.
If a film is trying to make some kind of "important statement", I think one grievous sin for me is when the substantiating of the statement is outdated. When I hear myself denouncing the "arguments" that the film is using and start rolling my eyes, it's obvious that I am having big problems with the film on an intellectual level, content-wise.
I have to emphasize again, though, that good filmmaking can (practically) always (partly) "save" the overall movie experience for me. Bad content is not necessarily a breakpoint for me.
What has art taught you about yourself that you never fully realized before, and are you happy about that? Have movies reinforced your fears and prejudices or have they freed you from them?
Art has taught me a lot about myself. It has mainly showed me how close-minded a person I was (and still am today for a large part) and it has exposed my infinite arrogance. Art has also made me perceive, feel and think about many things in manners that I never even realized the existence of before. It has made me a richer person with (I think) a greater understanding of his own ego.
I think movies have partly freed me from certain prejudices I had in life, while making me think deeper about the ones that I'm not exactly freed from (yet). Great art never really reinforces. It should always confront even when the ultimate message might be reinforcing.
If you think you only respond to films in non-political ways, what is it about your essence (or "youness") which formed that way, and does it make you more likely to constantly change your opinion?
Cinema has turned me into a wandering philosophical (and political) paradox, in a sense. The more thought-provoking and convincing arguments and ideas I get out of the many films I watch (or books I read) from different sides on the philosophical and political spectrum, the more and less political I become at the same time. I know more and therefore I know less. The flexibility of my mind increases.
I hope that last bit makes sense to you all. I'm pretty sure at least some people will relate to the sentiment of it.