[Sethomas]

the Christians weren't running around slaughtering civilians, especially not Christian civilians.

You're neglecting what happened when the first Crusaders arrived at Constantinople three months after Urban II's Deus Vult speech. Thousands were massacered, mostly Eastern Orthodox Christians and Jews. From 1090 onwards, I think it would be fair to say that the relationship between Western Europe and the Bynzantine Empire was fairly amiable. Remember that the first Crusade was begun to avenge "our brothers in Christianity" (or something of that sort) who died in Jerusalem... they certainly weren't Roman Catholic. The popes continued to try to make amends with the East well into the late fourteenth century, so animosity between the two sides on religious grounds was really quite negligible. My impression has always been that the Bynzantines were largely ignored simply because their power was decaying so rapidly that the Westerners didn't need to take them seriously.

Oh, and I think the Templar stronghold at Acre fell in 1296, not 1290.