Multiethnic armies were the norm for crusades.

Crusades were usually pitched as a response to some horrible event that needed to be countered, such as the destruction of Edessa in 1144 or the loss of Jerusalem in 1187, and from then on the fact that Christian armies had failed to conquer it back. Commanders could rarely afford to be fussy on the grounds of ethnicity; any good fighter was welcome, and that's assuming they even wanted an ethnically homogenous army and I'm not aware of any crusader lord who did.

Crusade preachers and recruiters wanted a broad coalition of crusaders. Part of the thinking behind the crusades was that it could help bring the various political and ethnic groups of the Latin world behind a notion of Christendom; to think of Christians as a larger community that their more local differences should not overpower. This was rather successful, as crusading armies often tried to put their differences aside to 'enter the service of God' or 'join the army of the Lord', as crusade sermons often put it. On the Second Crusade, for example, a contingent drawn from communities across southern England, the Low Countries, and northern France assembled in the town of Dartmouth to set sail for the Holy Land. They swore to share all their loot, take decisions by voting, and that they were all in this together. Due to linguistic barriers the different ethnic groups generally kept to themselves (our sources for this group refer to 'Flemish ships' or 'English ships' etc.), but they did work together effectively. Enough people spoke Latin that communication could work between groups via multilingual spokespersons for each ship, even if not all the crusaders could understand each other. During the Third Crusade, different contingents wore crosses of different colours to signal the political loyalty they were aligned with, and a bunch of Flemings (who were neither loyal to the French nor English that dominated the contingent, but were tagging along) chose to wear green while the English wore red and the French went with blue. When Philip II of France left the crusade early, and Leopold of Austria also left, Richard the Lionheart was suddenly in command of an army of French, Flemings, English, Germans etc. Almost every crusading army was a multiethnic force, because crusading was an activity open to anyone good with a weapon, and the deaths or departure of leaders meant a diverse coalition could find itself under more narrow leadership. Even later crusades like those of Louis IX of France, which were very centralised for a crusade, had groups of non-French join the effort.

In the Holy Land itself, armies were also ethnically diverse just because the region was. There were the military orders which, like crusading armies, could not afford to be fussy even if they wanted to be. Crusader lords drew on the extensive Armenian diaspora, immigrants from all over Europe, as well as the indigenous Christians (themselves quite diverse). They tended to all get lumped together under the term 'Franks' because most crusaders were French, but the demographics of the Holy Land during the crusading period are a confusing mess. As the holiest place in Christendom, Christians from everywhere wanted to visit at some point in their life. The area was also a major centre of trade, dominated by Italian merchants but caravans from all over the place would come to trade in places like Tyre, Jaffa, or Acre. The trade boom caused by the allure of trading in the eastern Mediterranean even led to the gradual proliferation a new language called Lingua Franca (Language of the Franks). It was a grammatically simple trade language dominated by Italian and French, with loan words from a wide variety of languages, that lasted centuries and was spoken across the entire Mediterranean. If you were to take a walk through the towns of the Crusader States, especially places of economic or religious significance, you'd find groups of Germans, Ethiopians, Italians, Danes, English, Normans etc. You'd find a bit of everything Christian if you looked for it. In times of war, some of these men would join armies. It was entirely expected for a crusader lord in the late 1180s to have a few Germans or the occasional African in his army.

It would be a bit weird if they didn't.