This is almost equivalent to blaming the Russian Orthodox Church for the persecution of Catholics in the Soviet Union. Pope Innocent III encouraged a crusade, and the Fourth Crusade was the result, but he was not in control of it, and disapproved both of their sack of Zadar (a Catholic city) and of the diversion to Constantinople, and it was Frankish soldiers, who happened to be Catholics, and their leaders, rather than the Catholic Church, who were to blame for the outrages that took place.
Similarly, in WWII Croatia, it was Ante Pavelic and his Ustasha followers, who included some members of the Catholic clergy, but not the Catholic Church as an institution, who committed the massacres of Serbs, Jews, and others (including anti-fascist Croats); the head of the Catholic Church in Croatia, Archbishop Stepinac, spoke out publicly against the racist policies of the regime.