The use of “hadn’t” places it in the subjunctive (for those of us old enough to have been taught that), implying that there is a possibility that he could have failed to believe or that maybe he really didn’t believe but only pretended to. “Didn’t” adds to the confusion because you want to line it up with the “had” and make them serve a similar purpose. Actually, “didn’t” is present only because of the negation. In English, you cannot say “He believed not”; you have to say “He didn’t believe”. Consider the case if the two sentences were “If he had believed in that, none of it would have happened” and “If he believed in that, none of it would have happened”. Notice in this case that it is clear that there is some doubt as to whether or not he believed in the first sentence, but not in the second. In both cases, the second sentence also fails to make really good sense (either with or without the negation) because the if clause wants to be subjunctive and imply “maybe he did and maybe he didn’t, but let’s use what happened to help us figure out which is true”.