Precisely. The papacy may have been in the middle of the Hundred Years War, but the war was between England and France for control of French territory.
And while the Thirty Years War started as a religious war, in reality it soon became a political war between the French kings and the Hapsburgs (Holy Roman Empire).
Kings fought wars for land, because land meant money and power. They may have used religion as a pretense, but it was always about land, money and power. To believe otherwise is to ignore history.
There was a poster here on FR that rail about the “Lutheran Sack of Rome!” constantly. That seemed odd to me, since the Protesting Estates never really got on that side of the Alps that much, let along Rome. Well, it did happen, but it was by the Catholic HRE Charles V who had found that the Pope of the time was trying to support some of the Protestant armies against the French! So you did have a army of mercs, some who were Lutheran/Protestant, invade Rome. But they did it at the command of the Catholic Charles V!