The fourth crusade was wild.
- let's go and reclaim Jerusalem from those non-Christian infidels!
- Sure. We're gonna need a bigger boat. Let's ask the Venetians.
- Here are your ships, guys.
- Err, we have no money.
- Sigh. ok. Go and attack our rivals over there.
- The byzantines in Constantinople? They're Christian.
- You want something to do, or not?
- Fine. let's kill them all, boys.
Result: Constantinople is ravaged. Byzantine Empire fatally weakened. Ottomans take the city 200 years later.
It's a nice vibe history you've got going on here but unfortunately it has little to do with reality. I recommend starting with the disastrous reign of Alexios III who had drained Constantinople's treasury years before the Crusaders arrived to understand the bigger picture. Ransacking their own capital in the name of internal strife has been a Byzantine specialty since the Nika riots of 532.
"- Err, we have no money. - Sigh. ok. Go and attack our rivals over there."
Strictly speaking, this is not what happened, and a gross oversimplification. The Byzantines were not exactly rivals of the Venetians. The whole thing was quite bizarre in fact, Roger Crowley has a pretty good story of the events leading up to this in "City of Fortune: How Venice Won and Lost a Naval Empire" if I'm not mistaken.
There's no good guys in this situation. The Byzantine Empire spent 1000 years doing the same kind of shit to other people. The little people, of course, suffered tremendously for it.
They justified it by religion but they really wanted to rob and mug. And this happened many times across history and will continue to happen: people claiming they are fighting for an ideal but really just wanting to gain power and money.
Yes and no. Downplaying “honest” convictions and other motivations unrelated to greed is flawed. Plenty of people in history did what they did because they truly believed in it (of course there were usually several motivations)
For instance the first Crusade was organized as a military relief expedition by the Byzantine emperor and the pope to save the empire from Turkish invasion and liberate the recently conquered Anatolia. Jerusalem was mostly an aspirational and symbolic goal.
Most people who joined did it because of sense of duty and various degrees of religion fanaticism. There was little prospect of profit and while the expedition was enormously more successful than anyone could have anticipated the overwhelming majority of initial participants were dead by the time they reached Jerusalem. Even those that survived to the end didn’t necessarily profit that much.