I read a book some time ago titled "The Knights Templar: The History and Myths of the Legendary Military Order"by Sean Martin, and it mentioned that the Templars had a rather high tolerance of Muslims for the time, off of the battlefield of course. They even reserved a small prayer room in their head chapter house for Muslim visitors. I think the book also detailed an incident where a newly arrived crusader knight was in their hq, saw a Muslim praying in the small prayer room, tried to force him to stop, the Templar guards noticed this and threw the offending knight out of the building. I'm not entirely certain on the accuracy of the book's accounts, but did the Knights Templar have an unusually high tolerance towards people of Islam even during the crusades?
The anecdote you've described about the Templars safequarding a little prayer room for the use of Muslim visitors, comes from the memoirs of a Muslim source, Usama ibn Munqidh (1095-1188).
Whenever I visited Jerusalem I always entered the Aqsa Mosque, beside which stood a small mosque, which the Franks had converted into a church. When I used to enter the Aqsa Mosque, which was occupied by the Templars, who were my friends, the Templars would evacuate the little adjoining moseque so that I might pray in it. One day I entered this mosque, repeated the first formula, “ Allah is great, ” and stood up in the act of praying. Then one of the Franks rushed to me, got hold of me and turned my face eastward, saying, “ This is the way you should pray! ” The Templars came up to him and expelled him. They apologized to me, saying, “ This is a stranger who has only recently arrived from the land of Franks and he has never before seen anyone praying except eastward. ”
It's not beyond the realm of possibility that Munqidh experienced such an occurrence, but you should consider a few concerns. First, Munqidh was an aristocrat from the ruling family of Shaizar, an independent Muslim city which fell in and out of the political orbits of the more powerful political entities such as Antioch, Damascus and Aleppo. As a man of wealth and good connections, Munqidh may have enjoyed a degree of hospitality that was unusual. Second, Munqidh's anecdotes about the franks often take a comic tone, playing up foreigners ignorance into a sort of humorous buffoonery.
So where does that leave us? We have a lack of Frankish sources on whatever hospitality the Templars institutionally offered to muslims. We have a Muslim author who might have been unusually chummy with Franks, or who might have fictionalized the event for comedic effect. At the very least it says something, that the idea of templar hospitality was not so absurd as to be beyond the realm of imagination.
Source
Usamah Ibn Munqidh, “ Autobiography"