Bottom line. When you take the time to learn A piece of information you have scarified learn B, C, D, … in the same time slot. This opportunity cost creates that you prioritize you learning. If you let someone censor you, you are letting them set your priorities. Rarely can other people be trusteed to know what priorities are best for you; at least until we have a better understanding of neurology.

1.  Exposing yourself to information that's distracting; the act of reading the information is not the current best use of your time (TvTropes.)

I think of this case not as a case for censorship but for a case of priorities. TvTropes is fine as long as you have worked out all of the priorities ahead of TvTropes first.

2.  Exposing yourself to information that puts you or others in direct danger because you know too much (illegally reading classified gov't secrets; personally investigating a crime)

Well the importance of the information knocks it up the list in priorities and the potential down sides knock it down the list. If methods/techniques to circumvent the downsides are learned then it gets knocked back up the list.

4.  Exposing yourself to information that violates someone's privacy or rights (reading a secret diary; looking at pirated content)

There are good reasons in normal circumstance not to pry into other peoples privacy. In general it is so low a priority that finding out what life is like with out break Y persons privacy has a higher priority.

6.  Exposing yourself to "escapist" media that make the real world seem less appealing by comparison, and thus make you less happy (porn; some science fiction and fantasy; romance; lifestyles of the rich and famous.  A variant: plot spoilers, which can also ruin future enjoyment.)

You are human you need to enjoy yourself to be productive some amount of escapist media is just fine. I am not going to claim it is only ok if it directly increase you productivity, I think it is a complex issue that I am not going to get into further.

1. Exposing yourself to information that's likely to cause dangerous psychological damage (graphic depiction of rape if you're a rape survivor; writing that romanticizes suicide if you're depressive; pro-anorexia blogs)

2. Exposing yourself to information that might alter your character in a way you don't currently want (the argument that repeatedly seeing violence in video or photographic form makes us less compassionate)

Does X information bring benefit to you? Or rather the real problem is can you tell if they bring you benefit before they cause you damage. If you don't know if they can cause you damage then reading about X is probably not as important as find out how susceptible you are to psychological damage. Then once you have answered that question you can determine the priority of X information.

7.  Exposing yourself to persuasive arguments that might make you do things you currently consider morally wrong (Mein Kampf, serial killers' manifestoes)

1. Exposing yourself to content that might persuade you to do things you don't currently want to do (advertising, watching the Food Network if you're dieting/fasting; the sirens' song, if you're Odysseus)

9.  Exposing yourself to effective, emotionally manipulative arguments for things you're currently confident are false (possibly religious apologetics)

If you think that you morality can be so easily change then learning not to be unduly influence by arguments should be high priority for you. You are exposed to arguments that while irrational can be convincing if you do not think them through properly.

10.  Exposing yourself to "cynical" true information that lowers your utility/motivation/happiness in everyday life (public choice theory, if you're a civil servant; accounts of unsuccessful and dissatisfied grad students/law students, if you're a student)

If you are demotivated by reality then it should be high priority to learn how to be more realistic.

11.  Exposing yourself to content that's "disgusting" or "degrading" in your view (Two Girls One Cup; Tucker Max; gangsta rap)

Same as one.

Approximate Groupings

1, 11

2

3, 5, 7, 8, 9

4,

6,

10