In the case of the Albigensian Crusade, the Albigensians (who were a cult, not a population) declared war on their king under the leadership of the Counts of Toulouse. The King of France won the war and afterwards executed a thousand or so Albigensians and others whom he considered ringleaders of the rebellion. The Pope's representative, St. Dominic, protested the harshness of the King's response but was overruled by the secular authority. Pope Innocent did not celebrate or endorse the reprisals. He was glad that an unstable and antiChristian movement was ended, however.
The Inquisition was inaugurated by the Spanish crown in order to root out pro-Muslim fifth columnists. The Spanish throne considered Jews to be among this number due to their perceived collaboration with the enemy during the Muslim occupation. No entire populations were killed - 3,000 people were executed over a period of a century for crimes ranging from assassination to apostasy. A good number of these executions were unjust and politically motivated. No Pope celebrated the Inquisition.
Protestants were persecuted in the Netherlands by Philip V because he felt they were plotting against his rule. Similar persecutions of Catholics were undertaken in England against Catholics at the same time - persecutions which were far bloodier and went on much longer. The Pope neither authorized or approved of Philip V's actions, let alone celebrated them. Philip himself considered them an entirely internal matter.
The St. Bartholomew's Day Massacre, like the Inquistion, the Albigensian Crusade and the repressive policies of Philip was politically motivated. Again, there was no genocide - remarkably almost all of the thousand or so Huguenots murdered were political enemies of the Medici family. The Pope celebrated the event because he was informed that a plot by Calvinist traitors to overthrow the Catholic King of France was successfully foiled. Only later did he learn that he had been manipulated by the Medicis (and not for the last time). The Thanksgiving Mass he offered was not a gravedance over dead Protestants - it was a celebration of the survival of the French monarchy.
No Pope has ever presided over genocide. Protestants such as Cromwell and freethinkers such as Stalin have attempted genocides against Catholic populations. This doesn't give me license to accuse prominent atheists or Protestants of those crimes.
That's the real history - your implied portrait of Popes ordering hits/dancing for joy over people's deaths is highly inaccurate.
The Pope Innocent III excommunicated the Count of Toluse because he would not commit the murders. Simon de Montfort had no such problem and committed the atrocity.
St Dominic founded the Dominican order that held sway over the Inquisition.
The Pope had blood on his hands