Well, one might ask what, exactly, does your question mean by "censored". Often the word means something as common as preventing small children from viewing material they cannot deal with. Or it can be as extreme as book burnings and jail time for the artist. Each person answering your question has their own idea of what they think you're asking & what they think others are answering, but they may be wrong.
here's no broad "should" or "should not" for art censorship. You need to look at specific cases-- it's an issue of artistic meaning, context, institutional power, and platform. I work in the Museum field and the conversation surrounding how monuments of racist leaders were being vandalized by protesters in the US a few years ago really highlighted the complexity of "censorship."
In my opinion these vandalized monuments would, ideally, be removed from public spaces and re-contextualize within museums with the vandalism and protest as a part of its new meaning. I wanted this to happen because as public monuments to racists, these artworks empowers White Supremacists while at the same time disempowers marginalized people. If taking the statue away from a public place and/or recontextualizing an art piece is "censorship" then I am pro-censorship in this case.
Which leads to a more important point-- censorship is also often an issue of platform/ space. Unlike some people who saw the irreparable damages done to these statues as another form of "censorship." I am ok with their vandalism because 1) these monuments belong to dominant history; U.S institutions have given the stories behind these monuments so much platform tat their destructions do little to erase their story. Eeryone knows who Columbus is; tearing down his statues won't change that. 2) These monuments take up space that could belong to other stories that were "censored" by virtue of being left out of histories. People were up in arms about how protesters were destroying the "histories" represented by these monuments, but they never considered that these protesters' histories weren't represented by any monuments. Their act of vandalism is an act of monument-building in itself.
To be straight forward, these monuments were given their platform by a bunch of powerful White men a long time ago to forward a White Supremacist agenda. These men also actively deplatform stories of any marginalized groups, which in itself is an act of censorship. When talking about censorship, it's important to consider what power gives the art platform, what has already been platformed, and what has already been censored.
I do not want art to be censored, and recognize the problem with allowing one side and silencing the other. You said that speech you agree with doesn't need protecting. That is untrue. Minorities and victims are voices often silenced and it is their voice that needs to be protected.
When it comes to not tolerating the intolerant, that is meaning to speaking up against hate speech which is used to silence and harm victims and minorities. No it is not being hypocritical to stand up against intolerance. It would be hypocritical to NOT stand up for what you believe and for equal rights of all.
As to how this relates to the censorship of art. Art is a reflection of the artist and the artist's audience. As much as I do not want art that glorifies the demeaning of humans, I also know that there is a reason to allow this hate.
Trying to silence and hide artists who are Nazi's or white supremists or bigots or homophobes, is not a solution. It is the same as looking away or pretending that it doesn't exists. In order for someone to believe that there is a real threat, you need to know what the threat is.
This doesn't mean to parade hate speech for all to see. Anarchy isn't an viable solution. It means you can boycott and protest the art that is encouraging hate.
Complicated, but good questions. 
To answer them in short:
Yes, some art should be forbidden, quickest examples: porn of kids, art where it is known that the model(s)/artist(s) were abused/forced to do it, where art is directly calling for violence/killings/etc. Things alike should be not tolerated and forbidden by law, in my opinion.
Regarding censorship. It depends on the target audience, art accessibility and FYI trigger warning about the content.
If the art is meant for adults and it can be accessed by adults only - no censorship is required (only FYI trigger warnings required so that people could make an educated decision whether to click or not). If the art is meant for underage kids, ideally it shouldn't have any trigger content (or in exceptional cases - very light, marked with warnings before entering/viewing).
If the art is meant for both kids and adults and the art does contain trigger content - it must at the very least contain very clear trigger warnings, recommendations not to read for underage kids and why. The particular site could forbid the underage kids to read the trigger content (e.g. by utilizing the age info from profile form), or enforce 2 versions of the art (one accessible by kids only and censored, the other version uncensored for adults only).
In short: as long as the content is not meant for kids, the art should not be censored, but entail trigger warnings where applicable.
The owners of the site decide on the rules for content on their site, of course.
That being said, if the site/art is meant for adult content (and has clear trigger warnings), it should not be hunted down for containing NSFW art for the sole reason that 'kids could find it'. The kids (and everybody else) take responsibility for their actions the second they choose to disregard the warnings and proceed to click to the adult/trigger content.
Absolutely, but the point is their voices are often silenced because it's speech that some people don't agree with. So prioritizing protecting the voices you don't agree with, as a general rule instilled in all people, is what protects minorities and victims' voices :]
But yeah, the solution isn't to ban hateful stuff (unless it directly calls for harm which is apparently already covered by other laws). Let the hateful stuff exist, but point to it and say 'this is harmful in X Y Z ways, do not look at it if you are vulnerable to X Y Z' :]
EDIT:
I know you're not - I am :] To combat our biases, I think it's necessary to actively prioritise the ideas we disagree with; if we think we're treating them 'equally', chances are we're actually favouring the ones we agree with. “When you're accustomed to privilege, equality feels like oppression" - this is the generalization of that idea.
I wasn't saying one be prioritized over the others. And yes Protest boycott and make it clear that hate isn't tolerated.
There is a huge difference between making art and harming others using art as an excuse.
This is an example of the latter. This is not art, this is abuse and child exploitation.
That's kinda where discussions can get "interesting" - some people assert that no one has the right or authority to designate anything as art or not-art except the artists themselves. But there are some things, like this, that pretty much everyone feels should be recognized by the public as not-art. So, how does society decide what is "unquestionable art" and "unacceptable art", and who gets to do the deciding? Don't feel obligated to answer, I intend that to be a rhetorical question & it's really a different issue than the one raised in this thread.
As a matter of fact, I don't support unrestricted free speech, precisely because of this. You do understand that there is no legal definition of hate speech in the United States, yes? I don't think I need to explain the danger of having something so unbelievably vague left up to the supreme court to decide on when, "I hate potatoes" can be just as easily lumped together with, "I hate this minority group."
"So when you have a site like Tapas or Webtoons that doesn't want sexual acts on it, that is their right to not have it."
This is not even the same class of censorship. Freedom of speech laws don't restrict private institutions from restricting what content they allow on their platform. The exact wording of the 1st amendment explicitly states CONGRESS may not restrict it. It only protects you from legal trouble. You still are not protected from freedom of societal consequences. You can still lose your job or get your ass kicked over something you say. It would be foolish for someone to think that because the government cant arrest them that they can say whatever they want with no consequence.
"In other words "free speech for speech I agree with". That's a slippery slope you are living on..."
This is not the win you think it is.
I think the easiest solution is to just not put 'art' on a pedestal. Something can be art, abuse and child exploitation ALL AT THE SAME TIME. It's still wrong - calling it art or not-art won't really make a difference.
It's also related to the tendency to dismiss something as having 'no artistic merit' (i.e. not worth studying, analysing or paying attention to) because its creator was a terrible person. If something was a product of abuse and exploitation, we should destroy it, but don't insist that 'nothing of value was lost' and shame anyone who mourns the loss of any insights the work may have contained (as long as they're respectful to the victims and agree that destroying the work was a regrettable but necessary course of action). Saying that something had interesting artistic insights is not the same as defending it morally, but it can be hard to see if you think 'art => good' (and therefore 'bad => not art', and in turn 'claim is art => claim is good')
Also, not putting art on a pedestal means people don't get to use art as an excuse to do terrible things. It's only an excuse if people excuse them for it!
ok freedom of speech does apply to some private companies if they have certain dealing with the government. And I don't want anyone deciding what "hate speech" is. Because what hate is to one is just vulgar to another, and to others is a non-issue. You don't want the government deciding that, or society for that matter. and 51% of the population forcing 49% to do something is horrid. Worst is a vocal 10% that knows how to ruin your life.
You're sort of touching on why a pure democracy (some call it true democracy) can be a nightmare.
But, we're drifting into politics & the OP may not appreciate the thread going there.
As long as the discussion (drifting into polictics) is not drifting into people fighting everything is ok
There's a line that had to be drawn when it comes to trying to emphasize with intolerance. Like, if you're using freedom of speech to say things that are actively harming the use of freedom of speech, I think it cosmically and unanimously defeats itself.
So, like, uh...We need to tolerate each other for our freedom of speech to simply even exist. When we use this freedom to create and spread intolerance, we are harming the very core of what the amendment is even for.
I think art shouldn't be censored, but we should put a TW on some sensitive scenes and a +18 to avoid children sees some things they can't understand and can cause them trauma or anxiety
