"Art" describes such a diverse range of human activity and products that objectivity is certainly needed for effective evaluation of it. However, I agree with previous posters who mentioned that there should still be some established guidelines or standards for determining why a piece of art is truly art, and what makes it a great piece of work in historical and modern day context. Far too often these days everything that is created is categorized as "art" with no standards as to why it should be called art.
Are you asking about objectivity from the viewer's perspective or from the artist's perspective? If from the viewer's perspective, objectivity has a role in evaluating contemporary art, which is highly subjective. For instance, if some photography exhibits from the recent past are viewed subjectively, they may be discounted and rejected out of hand, while if viewed from objective standards of composition, etc, they may be evaluated as good or bad art. On the other hand, the same exhibit--if viewed objectively from social and moral standards--may be rejected as a violation of the idea of art, which is historically connected with form and beauty. So objectivity from the viewer's perspective on contemporary art can have importance from more than one point of view.
The short answer to this question is "like or dislike is not the only point of responding to works of art".
We can look at a painting and say right away if we like it or if we don't, however, simply stating our emotional, subjective response will not 1) give us any insight into the artist's intentions, 2) help to generate a discussion on the meaning of a work, or 3) deepen an individual's relationship with the piece specifically or with art more generally.
Art is a conversation. When we have a debate on any issue, we will always be served best by making points and exchanging ideas as opposed to moving away from the discussion by simply determining sides and then taking one.
Being objective allows the discussion to be nuanced and interesting in ways that subjective approaches sometimes can't.
Indeed, a knowledge of art history is essential, providing a frame of reference and a point from which objectivity can emerge. For, as in all forms of artistic venture, there is always something of the artist in the art, and knowing the penchants experiences, and background of the artist as well as the techniques which he/she employs assists greatly in understanding of a contemporary work.
In my many years of teaching students, and even with my own children, we had discussions regarding how to consider contemporary art. My best method of explanation came to be making sure they all had some basic knowledge of art history and art in context. If one understands why the art was made and how it reflects the events surrounding it, one can begin to accept its existence.
Contemporary art usually is trying to give a message in a new way. Perhaps using a new material, changing the size of images, or just restating an opinion in an unexpected visual manner is meant to bring an issue to the attention of a certain group of people.
This is a good question. When it comes to contemporary art, we are on post-modern intellectual footing. This is to say that there is a questioning of all past standards. The idea of standards is thrown out the window and there is even sense of suspicion with even the mention of standards. The only absolute is that there are no absolutes. When it comes to art, this idea is pushed to its logical limit. All things are seen a relative.
Some critics say that if we view art in this way, then we do away with the idea of art. In other words, if everything is art, then nothing is art. Critics of this way of thinking still want to hold onto some semblance of objectivity, namely what makes a certain piece of art worthwhile and excellent.