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.