is it meet, think you, that we should also, look you,
be an ass and a fool and a prating coxcomb?"
You partake in a piece of media. Frankly, you find it to be just terrible. The acting is wooden, the plot is boring and unrealistic, the effects are cheap, the soundtrack is annoying, and the costumes are ugly.
Worse yet is the Aesop the show attempts to give: The logic of its arguments is faulty, if not nonsensical, its world-view is unnuanced, the characters frequently burst into boring monologues concerning what are almost certainly the author's opinions on the subject, those who disagree with the opinion are dismissed unsatisfactorily, and the general preachiness makes it a chore to get through.
And the worst part? You actually agree with what the work is trying to say.
Related to the concept of the Clueless Aesop, Don't Shoot the Message is the phenomenon that results when viewers feel the need to explain that while they are in agreement with the message attempted by a work, they hate the delivery (typically for being anvilicious) enough that it is still intolerable. They might consider the messenger to be Right for the Wrong Reasons, or the message to be too oversimplified or laden with straw. The work is seen as preachy, even to people who agree with the message. The above description gives an extreme hypothetical, but you do not need to think something is So Bad, It's Horrible to qualify: Merely dislike it for any of a hundred reasons unrelated to its Aesop.
Such a position should not be seen as particularly incongruous, but it is often assumed that those who dislike a work necessarily disagree with its point of view. Many times, it is indeed the case: If an unpalatable bias is detected in a work, people will steer clear of it. However, the a priori assumption that this is the case is most certainly an invocation of Logical Fallacies — for instance, hating a corny anti-drug PSA does not mean that one is a heroin addict.
The lines have been further blurred with the rise of entertainment specifically designed to appeal to various spots on political and social spectra, and not others... style mixes with substance to such an extent that a rejection of one is seen as a rejection of the other. To take several broad examples: Certainly there are conservatives who dislike Ann Coulter or Glenn Beck, and liberals who dislike Michael Moore or Keith Olbermann. There are fundamentalist Christians who can't stand the Left Behind series or Chick Tracts, and atheists who don't like having Sam Harris or Bill Maher as spokesmen. There is, of course, nothing objectively wrong with liking any of these things (yes... even that one). However, the fact remains that those that like the politics, but not how it is presented, often feel the distinct need to mention the fact. This tends to pop up within natter upon this very wiki, as if the mere fact that someone has problems with the Roman Catholic Church lends more credence to his negative opinion about The Da Vinci Code.
One possible form this could take is a Space Whale Aesop. Contrast this with Strawman Has a Point, when one can't help but agree with something like the opposite of the work's position (though not so much because of one's prior beliefs as because the work did such a bad job of portraying the opposition). This could also lead to a Logic Bomb if your reason for shooting the message is because of the messenger's hypocrisy. Compare Stealth Parody, which can differ from this trope only in creator intent, and due to Poe's Law may be confused for each other. See also Fallacy Fallacy, when a perfectly cogent argument gets wrongfully dismissed as being "wrong" just because it uses a fallacy.
Also related to Hitler Ate Sugar, when a viewpoint is criticized on the (fallacious) grounds that someone who held it was a bad apple. Those too eager to avoid this characterization may resort to the No True Scotsman fallacy ("that person isn't a real example of X").