I agree it's foolish to attribute the Holocaust to the Mufti. But that's not to say he did no harm, whatever his private feelings in the matter. First, the degree to which he encouraged & instigated the Great Arab Revolt of 1936 led Britain to virtually close the doors to Jewish immigration in '39, just as their need became most dire. Then he persuaded Hitler to prevent further Jewish emigration from the Reich or territories into Palestine. Again, as their need was most intense.
Of course, one might say the US or Britain might have opened their doors, but after the war's outbreak they at least had the argument that Jews coming from the Reich were enemy aliens (even if technically stripped of their citizenship by the Nuremberg Laws). This was not so for Palestine.
How many lives were lost because Palestine was no longer open we'll never know. But you have to give Haj Amin al-Huesseini credit, virtually singled-handedly he caused Britain & Germany to collaborate ... all while locked in a deadly war!