In general the Frankish legal systems put the local Muslim populace as the lowest of the low. However Phillip of Novara has highlighted how in cases where there were no other witnesses for legal cases, the local Muslims were deemed okay for giving evidence.

Additionally, local Lords knew that keeping the locals on side was a good thing. Tax reductions for local farmers were introduced to make sure they would be more likely to stay and not move away to Muslim neighbours. Keeping their loyalty was something for the Lords needed, especially if the farming and trade required it.

William of Tyre was such a poulini, and makes comment on how he had a wealth of Muslim friends in which he kept company. This is also reflected in the accounts of Usmah Ibn Munqidh, where he was appreciative of the 2nd gen crusaders since they were much more nicer and understood the society a lot better., he quotes 'they are the exception and should not be considered representative'. He even recalls how two templars had to take away a brand new crusader since he was making a fuss towards the Muslim populace. The templars even apologised for his misactions.

Ibn Jubayr, a Muslim pilgrim who travelled to the east in around 1184 also made comment on how despite the segregation of Muslim and Christian communities, crops and animals were communally shared out and 'no wrong takes place because of it'.

Generally speaking though, the modus vivendi between the two faiths was that of just ignorance and compromise. If you want to discuss it more, I did my dissertation on crusading interaction so happy to answer more if you require

Sources

Peter Exbury, cultural encounters in the Latin East, John of Jaffa and Phillip of Novara, in Kurt Villads Jensen, Kirai Salomens and Hell Vogts, cultural encounters during the crusades, 2013, pp- 229-236.

Usman Ibn Munqidh, book of contemplation.

William of Tyre, multi works. The great deeds beyond the sea being the better.

Johnathon Phillips, the crusades 1095-1204, Ibn Jubayr, The travels of IBn Juyabar, p. 230