Ummm... Wut?
There is absolutely no evidence whatsoever that Rome was trying to deliberately undermine the Eastern Roman Empire.
Contextually speaking, everyone involved in the Crusades would have understood the threat posed by the "Saracen" and the "Turk" to the Christian world.
Everyone wouldn't even have been bothered, let alone informed upon anything, had the Pope not lit the candle, figuratively speaking.
Since the threat did not exist.
I'd wager that not even the inhabitants of Constantinople were all that bothered, seeing how Byzantium had arranged itself with the by then (shortly before the call for help) long since rivalling Seljuk mini-states (emirates) that Byzantium was successfully playing against each other to its own gain and to their detriment.
I repeat, the capital was under no threat, the Seljuks of Manzikert having split into various rivalling factions that could never have co-ordinated into yet another promising assault.
What prompted the call for help was Byzantium having finally countered the far greater peril of the Norman invasion of Epiros and Macedonia (by finally winning those territories back and driving the Normans out) and now seeing an opportunity of recovering lands taken by the Turks after Manzikert, but preferring not to go it alone.
To address this threat to Europe overall, Sicily had fallen from Saracen rule way before the very first crusade (to the same Normans), Saracen raids on Sardinia had ceased, Bari had fallen back to Christian rule more than 200 years prior and Cordoba had fallen 60 years before, effectively more than halving Muslim holdings in Spain. The threat to Europe as a whole (if it ever existed at all) was not there.
So we can indeed assume that most those following the Pope's call to aid Byzantium were, as usual with ulterior and very worldly motives hidden under the conveniently fluttered flag of saving Christianity, duped into religious zeal and thus driven by it. That never made the Crusades into a religious campaign though, no matter how the usual gullibles continued believing that. I doubt that Bohemond was one of those naive when he took Antioch as his own prize and kept it to form a monarchy that outlasted both the Norman monarchies of England and Sicily.
Nor Baldwin to form the comparatively short lived kingdom of Edessa.
The whole point being, so as not to bore the more disinterested with excursions into REAL history, that the Crusades do not serve, historically, as a convenient hook upon which to hang Christianity for a bashing along the lines of "we wuz as bad a they be".
Best to not go down the path of incomprehension that this
See above. Crusade is not the poster child for your cause in defense of islam and radical muslims. Get over it.
signifies.
They cannot serve in defense of anything, just as by that time the Arab speaking Muslims that some try to project into today cannot serve either. The Seljuks had completley squashed the Arab speaking world of the M.E. by that time.
This sort of thing happens when people try to interpret history only along the lines of their political agenda of today, they cease to see the actual events even when those are spelled out for them. I was ironically, even where I have no cards in that particular game, effectively defending Christianity by default. Certainly refuting the original post that brought up the Crusades in the first place.
Driven, sure. Motivated, nope.