I’ve written a few answers to similar questions in the past, but instead of linking to all of those I thought I’d write a new answer, so all the info is in one spot!

There was a lot of diversity in the inhabitants of the Kingdom of Jerusalem. The Latin (or “Frankish”) crusaders who established the kingdom found Greek Orthodox Christians who followed their own patriarchs in Jerusalem and Antioch, and ultimately the patriarch in Constantinople; Syrian Orthodox, who spoke Arabic or Aramaic and also had their own patriarchs, and whom the crusaders called “Jacobites” (typically known as Assyrians today); Maronites in Lebanon, who eventually united with Rome later in the 12th century; Armenian and Georgian Orthodox, speaking their respective languages and following their own patriarchs (the Armenians had one in Jerusalem as well); and Christians from further east in Asia, whom the crusaders usually called “Nestorians” (i.e. the Church of the East, with its patriarch in Baghdad). They also knew about Coptic Christians in Egypt, and Nubian and Ethiopian Christians, who were dependent on the Coptic patriarch in Alexandria. And of course, while the crusaders were there, there was a Latin population with their own patriarchs in Jerusalem and Antioch too.

At the time of the crusades, Jerusalem was controlled by the Shi’ite Fatimid caliphate in Egypt. The Seljuk Turks (who were Sunni) had captured Jerusalem from the Fatimids in 1070, but the Fatimids took it back in 1098 while the Seljuks were distracted by the crusade further north in Syria. The Fatimids lost it again to the crusaders in 1099.

As for population, according to the Persian traveller Naser-e Khosraw, the population of Jerusalem before the crusades in 1050 was about twenty thousand Muslims, Christians, and Jews of all denominations. One modern estimate by Josiah Russell gives 2.3 million people in eleven thousand villages in all of Syria/Palestine, 360,000 of whom lived within the Kingdom of Jerusalem (and 250,000 of them were living in rural villages). A reasonable assumption, maybe, but as Ronnie Ellenblum argues, there’s actually no way to know how many people there were - we could perhaps guess at the number of adult men, but in particular we have no information about family sizes. How many women and children were there? How many were Muslims, Christians, Jews? We have no idea.

So with that in mind, here is what we do know about the various religions in the crusader kingdom.

Eastern Christians

Armenians

There may have been Armenians living in Jerusalem as early as the 4th century, when the Armenian kingdom converted to Christianity. The Armenians were on the border of the Roman/Byzantine Empire, and were sometimes persecuted by the church in Constantinople, especially after the Armenians and other eastern churches split from Rome and Constantinople in 451. They may have even benefitted a little bit from the Muslim conquest of Syria and Mesopotamia in the 7th century, since the Caliph Umar recognized them as a distinct community, separate from other Christians, and allowed them to appoint their own patriarch in Jerusalem.

Most Armenians lived in northern Syria/eastern Anatolia/Mesopotamia, and they were friendly to the crusaders. Armenians may have been the majority in the first two crusader states that were established in the north, in Edessa and Antioch. The ruling family of Jerusalem in the 12th century also had a strong Armenian background, through King Baldwin II’s wife Morphia of Melitene (Baldwin II had been Count of Edessa before becoming king). Their daughter Melisende became queen of Jerusalem, and two of their other daughters also married into the ruling families of Frankish Tripoli and Antioch. During Melisende’s reign, the Church of the Holy Sepulchre in Jerusalem was rebuilt (i.e. the building that currently exists there), and a book of Psalms (the “Melisende Psalter”) was produced, which has lots of Greek and Armenian artistic influences.

Thanks to the disruptions caused by the crusades in northern Syria, the Armenians were able to establish their own kingdom in Cilicia in southern Anatolia. For awhile, at the end of the 12th/early 13th centuries, the Armenian church even united with Rome (but not everyone was happy and the union didn’t last long).

In Jerusalem, this was probably the period where a distinct Armenian quarter took shape, built around the monastery/cathedral of St. James in the southwest part of the city, near Mount Zion. The current cathedral of St. James was built during the crusader period in the 12th century. The boundaries of the four modern quarters of Jerusalem only date from the 16th century but the Armenian quarter already had its own wall before that, so it wasn’t absorbed by the other Christian neighbourhoods.

Georgians

Georgia was a somewhat exotic country to the north, even further away than Armenia. The crusaders didn’t know much about it, but they had a common enemy in the Seljuk Turks.

There were Georgian monks and nuns in Antioch and Jerusalem, and it was probably through them that the crusaders were able to contact the kingdom of Georgia in the north. King David IV of Georgia, apparently with help from 200 crusader knights, defeated the Seljuks at the Battle of Didgori in 1121. Georgia also benefitted from the Fourth Crusade in 1204, when the crusaders conquered Constantinople. Georgia supported the creation of a Byzantine breakaway state in Trebizond on the southeast coast of the Black Sea. Trebizond was basically a tributary state of Georgia though. This meant that it was now easier for the rest of Europe to contact the Georgians. The Georgians were planning to help with the Fifth Crusade against Egypt, but they had their own problems - first the Seljuks, and then the Mongols.

According to the Latin crusaders the Georgians “copy the Greek rite in almost all ways.” The crusaders also noted that

“They are very skilled warriors, and take immense pride in their beards and their hair which they grow a cubit [c. half a metre] long” (Hamilton, pg. 121)

But they had their own patriarch in Georgia and didn’t actually depend on the the church in Constantinople. They were among the churches that had broken away from Rome and Constantinople in the 5th century.

Syrian Orthodox

The Syrian Orthodox had split off from Rome/Constantinople in the 5th century. Their liturgical language was Syriac or Aramaic, and today they are typically called Assyrians, but at the time of the crusades they were usually called “Jacobites”. They usually spoke Arabic, the language of their Muslim rulers, so at first the crusaders might not have been able to distinguish Arabic-speaking Christians from Muslims, and they may have sometimes been attacked and killed along with the Muslims. There were Syrian Christian villages throughout the kingdom, with their own long-established social and political hierarchies, and the crusaders mostly left them to govern their own affairs.

Syrians could also rise quite high in crusader society. There are many examples of Syrians owning property, becoming knights, serving in the army, intermarrying with Catholic crusaders, and working as doctors or merchants. The most famous examples is probably Saliba, a wealthy Syrian merchant who made his fortune selling wine. In 1264, Saliba fell sick and wrote a will, in which the value his property was evaluated as “475 Saracen bezants”, some of which he left to his family, who included Nayma (his sister) and Stephen (his brother), and various children and nieces and nephews, such as Catherine, Leonard, Thomas, Agnes, and Bonaventure. These names sound pretty European, so it’s likely that they were actually a mixed Syrian-Frankish family.

Saliba also owned several slaves, some of whom are named in his will:

“...to Maria, my baptized slave, [I leave] forty Saracen bezants. Likewise, I emancipate Ahmed and Sofia, my slaves, and I command that the aforementioned Ahmed and Sofia become Christians.”

Another baptized slave, Marineto, is named later as one of the witnesses. I’ll talk about slaves further below, since enslaved Muslims were a common sight in crusader society.

Maronites

Maronites were originally Orthodox Christians in communion with Constantinople (and Rome), but they developed doctrinal differences and were condemned by Constantinople in the 6th century. Since they lived in the mountains of Lebanon they were largely isolated from the rest of the world and developed independently of their fellow Christians after the Muslim conquest in the 7th century. During the crusades the Maronites lived not in Jerusalem, but entirely in the Frankish County of Tripoli, where they were pretty much the only native Christian group. They weren’t always friendly to the crusaders at first - in the early years of the county, they sometimes attacked the Franks, who sometimes retaliated.

Eventually however they agreed to unite with the Roman church, and unlike the Armenians, they are still in communion with Rome today. During the crusades the Franks considered them valiant warriors and solid allies. They were mostly expelled from Lebanon when the Mamluks conquered the crusader states in the late 13th century, but some of them returned, and some of them fled to the other crusader kingdom on the island of Cyprus.