The Roman Catholic Church's involvement with the sack of Constantinople in 1204 was limited to the Pope refusing to authorize the leaders of that sack with any ecclesiastical authority or approbation - in fact one of those leaders was excommunicated before he even set foot in Greece.
After the sack, the Pope officially condemned these two men in writing and interdicted them and their troops, cutting them off from the sacraments.
The army that sacked Constantinople was largely composed of Orthodox Christians who were settling an internal dynastic dispute.
The sack of Constantinople had nothing to do with Catholicism or the Crusades, and John Paul II's statement of regret and revulsion over some of the sackers calling themselves "Catholics" was a very generous gesture, given the fact that his predecessor Innocent III had already roundly condemned the action eight centuries before.
I believe the 4th Crusaders were doing the bidding of Venetian merchants who had financed their Crusade. In return these merchants wanted Constantinople removed, or at least seriously degraded as a merchant center. this would open up trade for Venice which, as is well known, would trade with the Devil or Islam for a profit in Ducats.