Initially, Crusaders took a very harsh stance with Muslims, which were often expelled out of cities, enslaved or killed, as during the fall of Jerusalem in 1099. With the conquest, an exodus of Muslim from both cities and countryside took place, which was made relatively easy giving most of the population was still probably Christian overall.For Latins, it was less an issue of ethnic or religious cleansing than getting rid of previous elites, even if the religious aspect shouldn't be neglected, especially regarding Jerusalem.

Still, even at this point, Crusaders had Islamic partners, such as the emirs of Homs, Shaizar and Tripoli which gave tributes to invading Franks before the fall of Jerusalem. Relations could be made on a more or less strictly political level, as long newly made Latin States could be ensured (the hostile policy of Tripoli led to its conquest).

Native Christians weren't Orthodox safe for the melkite minority (melkite meaning "from the king" aka the byzantine emperor) mostly present in the southern part of Latin States, but mostly Jacobites and Armenians (both following a non-chalcedonian credo, while Latins and Greeks followed a chalcedonian one). They probably were the main religious denomination in Syria/Palestine before the Crusades, not unlike what existed in Egypt.

The First Crusade represented a double opportunity : first, to get rid of an Islamic political and cultural elite that maintained them as second-class denizens (in fact, some were expelled from cities, rulers fearing that they might ally with Crusaders just as Armenians did in Cilicia), second to prevent a Byzantine religious and political takeover.

Jews faced the same fate than Muslims initially : expulsion, enslavement, killing. It was less for religious reasons (while there was a widespread persecution of Jews in Rhineland with the popular crusade outburst, the noble's crusade didn't participated to these pogroms), than Jews simply sided with Muslims during the Crusade.

As the dust settled, Crusaders understood their situation : they were relatively few, reinforcement of the 1101's Crusade were defeated, and they couldn't hope rule a land that would ally to their neighbours.

So, began a practice of "rough tolerance" where religious and theological differences played more of a secondary role.Muslims were granted sort of a mirrored dhimmi status (although without the humiliating features that accompanied this status, noticeably interdiction of clothes or legal minority) and entered sort of a mix of allod and serfdom status economically by being ruled by their own qadi. They had, while not on an equal footing, a relatively unrestricted freedom of religion in Latin States compared to Christians had before CrusadesCulturally, Muslims and Christians likely tended to ignore themselves, the (mostly rural) Muslim population within a feudal frame relatively undisturbed as long they payed taxes. In fact, there was a serious temptation for Muslims peasants outside Latin State to outright emigrate there as the land lacked men and Franks were generally trusted enough to not oppress them.

Native Christians began really quickly a rough but mutually beneficial relationship with Franks. Edessa, one of the cultural capitols of both Armenians and Jacobites in the region, was a mess of Armenian principalities which for the most part banded up with Frankish rulers. Not really because of gratitude or submission, but because fighting each other for local supremacy, they banded up with foreigners to ensure their own power just as Armenians did with Byzantines before. Not to imply an harmonious relationship between Franks and Armenians, but it wasn't particularly different politically than what Latins had amongst themselves.Religiously, the theological differences between Latins, Armenians, Melkite and Jacobites were neglected either due to sincere ignorance, or due to sheer realpolitik : not only native Christians maintained their beliefs and obtained a greater freedom of religion (it seems that native Christian clergy blossomed during the period) but their clergy tended to be part of the religious-political sphere as well within Latin State, participating to mass (sometimes sharing parish or churches in rural areas) and generally treated the same than Latin clergy.Overall, there's several aspects of a fair mix between Latins and native Christians, and while keeping in mind that (safe arguably existing exceptions) rulers were Latins, native Christians made up a significant part of Crusader society, both socially and economically, and militarily (the nature of the military role of native Christians still being debated).

Jews were arguably treated a bit worse than Muslims, being more easily targeted. Jewish communities of Jerusalem, Jaffa and Rama largely disappeared and it's possible it dealt a critical blow to Karaite Judaism, whom main centre was Palestine.Nevertheless, there was a noted and maintained Jewish presence elsewhere in Latin States, along the coast and especially around Acre in connection with western Mediterranean Jews for all the Crusader's period, while Jews were forbidden to re-enter Jerusalem, which was a main reason for their support of Islamic reconquest of Palestine.

Interestingly enough, Samaritans seems to have enjoyed a culturally and religiously renaissance within Latin States.

The period of "reverse-dhimmitude" and "rough tolerance" was declining before the end of Crusader States, tough, as religious identities were more pitched against each other : Crusades provoked a more tensed antagonism between Christians and Muslims/Jews, the Fourth Crusade and the interventionist policy of Manuel Kommenos led to a greater religious and communal differentiation between Christians.