In ‘The Ethics of Belief’ (1877) William Kingdon Clifford gives three reasons for believeing that belief without evidence is morally wrong (quoted from the article):
every single belief has the capacity to be truly consequential
poor practices of belief-formation turn us into careless, credulous believers
we have the moral responsibility not to pollute the well of collective knowledge
I am always wary of arguments that conclude that we have a 'duty' or 'responsibility' because these are easily abused by others and almost always require that we act against our own self-interest, sometimes in devastating ways. But each of these can be seen in a way that aligns the collective interest with perosnal [sic] interest, and that's what gives them force.
I'm in agreement with Downes here, especially on the count of how statements about duty and responsibility are too often not about the cultivation of duty/responsibility within us and by us, but about the imposition of duty/responsibility as a proxy for other things, typically the preservation of asymmetrical power structures. (I almost typed "strictures", but that would work too.)
We often talk about how the artist needs to cultivate a sense of responsibility for what she chooses to put out into the world. The same goes for what they put into themselves, what they choose to let flower within themselves. Credulity is dangerous, especially when it comes in the guise of skepticism and is actually nothing more than cynicism. But we have few formal structures in our society to promote such things.
Most of us simply don't care what we put into our heads, and the history of trying to get people to be more conscientious about such things is rife with bad solutions. But I hold out hope that the chief reason for that is because we've only just now started to learn about how we might do it properly.