So in the 2003 build up to the Iraq war, European and US media obviously had highly different interpretations of reality. I think it is fair to claim that those interpretations contributed to the publics opinion, although this could be a case of "hen and egg" where (local) media tends to bias its interpretations towards what their target audience believes in the first place. Would it be conspiratoric of me, then, to claim that the political leaders of the US seemed to have a creative view on truth? Or that for any politician with ambitions to do some particular thing, there is an enormous gain to be had by swaying media your way, thereby getting the people to side with you?
As a cynic, I like to play games of "follow the money". In many classic conspiracy theories, you single out one (e.g. ethnic) group as "bad", and the thinking is that if we only put those in jail, throw them out of the country etc, everything will be good. This plays well into majority populations that are (perhaps) struck by unemployment, poverty, starvation, or the general feeling of being dethroned. I guess this is similar to creating an external enemy (i.e. going to war) in order to make your people more coherent. So (some) political leaders have potentially a lot to gain by those conspiracy theories.
But the moon landing? Who would "gain" by having it declared fake? Anti NASA-ers? It does not make sense to me, even ignoring the massive evidence that it happened.