Doesn't really make sense to "blame" the Islamic tribes/kingdoms for the fall of the Roman Empire. Perhaps some other power would have done the same.
Hard to play historical what-ifs, but let me try. By the end of the 13th Century, almost all Crusader holdings had been taken over by the Sultan of Egypt Baibars. He used his consolidated power to defeat the Mongol horde at the Battle of Ain Jalut in 1260, the first time a Mongol army had been defeated.
It's possible that if there had been no Islamic power at the time, either the Golden Horde or the Ilkhanate would have eventually swept the Eastern Roman Empire away. Or maybe not. Who knows?
You appear intent on blaming the Islamic kingdoms for the downfall of the Eastern Roman Empire. It's not at all clear that they would have flourished in the absence of Islam. It's likely they would have been swept aside by the Mongols.
Even otherwise, you realise that the body blow to the ERE wasn't struck any Muslim army. Constantinople was captured and looted by Crusaders in 1204, apparently on the Fourth Crusade. Though the Greeks recovered Constantinople a few decades later, it was a shadow of it's past self, left with the city, north Western Anatolia and parts of the Balkans. The Ottomans ended the empire in 1453.
Hard to play historical what-ifs, but let me try. By the end of the 13th Century, almost all Crusader holdings had been taken over by the Sultan of Egypt Baibars. He used his consolidated power to defeat the Mongol horde at the Battle of Ain Jalut in 1260, the first time a Mongol army had been defeated.
It's possible that if there had been no Islamic power at the time, either the Golden Horde or the Ilkhanate would have eventually swept the Eastern Roman Empire away. Or maybe not. Who knows?