Art is not offensive by default, it seems to me. I would say categorically that something does not have to be offensive to qualify as art. I expect this will be the majority opinion.
Art can be offensive. Again, if we are working on the level of semantics, I would say that something can be offensive (and/or ugly) and still be art.
Art is about expression. Art is an attempt to communicate, represent, or explore ideas and emotions.
According to Wikipedia, art is the product or process of deliberately arranging items (often with symbolicsignificance) in a way that influences and affects one or more of the senses, emotions, and intellect.
This definition allows for work of all sorts, from beautiful to profane. If we want to insist that art is aesthetically defined, I think we have to say then that aesthetic sensibilities are not necessarily concerned with beauty, but with "goodness" - a looser notion than beauty.