It is really irresponsible to be phrasing censorship as a "responsibility". Censorship is a tool of the weak and simple-minded so that they can maintain the illusions of a shared reality promulgated by whoever is in charge. The only responsibility should be towards the free and unadulterated flow of information, and yes, it is the individual's responsibility to make sense of that in a civilized fashion.

My only exception to this rule is for things that are irrelevant to seeker's intent to acquire more information, advertising falls into this bucket.