Hi! I actually wrote a research paper on this, but looked specifically at how the Holy Orders (specifically the Templars and the Hospitallers) weakened the Crusader States during the Third Crusade. My conclusion was that they did not themselves have the influence or power to directly have a negative impact, but exacerbated pre-existing issues among crusaders.

The impact of the chivalric orders may have been exaggerated; they were no doubt among the finest soldiers that the Christians could field. Saladin executed the Templar and Hospitaller knights after Hattin specifically because "they were his most determined foes among the Christians." (John France, "The Crusades and the Expansion of Catholic Christendom") However, they simply were not numerous enough to make a major tactical impact on the battlefield. Balian of Ibelian's distress at losing 140 Templars at Cresson reflects the fact "in the Holy Land during the twelfth century the number of knights present was remarkably small." (Edward Burman, "The Templars: Knights of God") Instead, the value of the monastic knights was strategic; in holding mighty citadels, these fortifications acted as force multipliers such that, even after Hattin, Saladin decided to avoid sieging the Hospitaller fortress of Marqab (Helen Nicholson, "The Knights Hospitaller"). From this, we see that the military importance of the Knights Templar and Hospitaller was twofold: 1. A legendary and well earned reputation, and 2. Strategically holding chokeholds. Once engaged in a major battle, these advantages were significantly diminished, in no small part because of their small numbers. The primary military roles of the Knights were defense, counsel, and spiritual leadership.

The greed of these two Orders did contribute to weakening the Crusader states. At least for the Templars, "booty was considered a legitimate form of income and provided the means to further the work of their Order" (Piers Paul Read, "The Templars"); this resulted in a failure at Ascalon in 1153 when the Templars did not let other besiegers take advantage of a breach to save the best loot for themselves. The Hospitallers were accused of launching the ill-fated 1168 attack on Egypt out of greed, and the Templars were accused of failing to provide adequate support because they were too preoccupied with raiding Saracen caravans (Helen Nicholson, "Templars, Hospitallers, and Teutonic Knights: Images of the Military Orders"). However, these were only individual cases; there were larger strategic problems that plagued the Crusader states.

Perhaps the greatest weakness to the Crusaders was a lack of Byzantine support. Given the Empire's strength and closeness, Byzantine support would have been vital to keeping the Crusaders from losing much territory. Nur al-Din, Saladin's predecessor, decided against attacking Antioch in 1162, "explaining that he did not wish to provoke the intervention of the imperial forces" (Jean Richard, "The Crusades"). Saladin further weakened the Crusaders by providing commercial privileges to Pisan and Genoese traders, diverting their trade to Egypt. This was essential to Saladin's ultimate strategy to "eliminate the Frankish presence from the coastal regions and reap the fruits of his victory" (Richard). A lack of international support thus crippled the Crusaders.

Ultimately, it was infighting within the Crusader states that caused the failure of the Crusaders. The counsel of the Chivalric orders was so highly valued that "In the second half of the twelfth century, the two orders’…masters served as members of the royal council where their voices had the same weight as those of the members of the nobility" (Jochen Burgtof, "The Central Convent of Hospitallers and Templars: History, Organization, and Personnel"). This was dangerous, because when Baldwin IV died, there was no central leader to hold back the knights; this was because the nobles had spent too long fighting among themselves to seize power. The Templar grandmaster had pressured the new King of Jerusalem to attack Saladin: "put aside their white mantles’ and sell and pawn all they had than lose this chance to avenge their brothers who had died at the springs of Cresson…Unable to stand up to Gerard of Ridefort, King Guy ordered the army to march at dawn" (Read), resulting in the disaster at Hattin. Guy had previously advocated a Fabian strategy to deal with Saladin; it is likely then that Gerard had been the reason for Guy's decision to strike out.

Ultimately, the chivalric orders did play a role in weakening the Crusader states. The states had inherent weaknesses, which were exploited by Saladin, and exacerbated by rivalries between the Orders, as well as greed and hubris. Without the Orders, the Crusader states would have fallen anyway; whether they would have fallen faster or slower is decided by whether or not they had an aggregately more positive or negative impact on the Crusades as a whole.

I hope that this helped!