I'm curious when these nations fought if they represented their own nations or changed their banner, repainted their shields or did anything to show they were fighting as Christians rather than their own countries. Thanks in advance!
They all fought under the banners of whichever king they were following. The English fought under Richard I’s banner, which apparently had a lion on it (fitting his nickname, the Lionheart), and the French and Germans fought under their own banners. (As a side note, it’s a bit anachronistic to talk about “national flags” at this point - nobles didn’t even really have coats of arms yet, although that sort of heraldry was starting to develop around this time. Richard’s lion flag was eventually adopted as a national symbol for all of England, but it was just his personal banner at the time.)
There was actually an incident involving the different flags in Acre during the Third Crusade. When the crusaders captured Acre in 1191, Leopold V, Duke of Austria, tried to hang up his banner alongside Richard’s. Leopold was the highest ranking leader of the German contingent, since the emperor Frederick I had died on the way there, but Richard didn’t think that some lowly duke was worthy of flying a banner alongside his, so Richard tore it down.
Leopold took his army and went home, and when Richard was on the way back home the next year in 1192, he had to pass through Leopold’s territory and Leopold took him hostage. Richard was a prisoner in the Holy Roman Empire until 1197, when England paid a massive ransom.
There are some other mentions of crusaders fighting under certain flags, although they’re kind of rare. The Kingdom of Jerusalem fought under a standard that had a gold cross on a white background, or they were noted for carrying a relic of the True Cross at the head of the army. The Templars and Hospitallers were known for their distinct emblems on their uniforms, if not their banners. But when crusaders from Europe showed up they brought their own banners with them, there was no overall “crusader flag”.
Even nobles within the crusader Kingdom had their own banners and proto-coats of arms. During the Seventh Crusade, the French chronicler Jean de Joinville mentions a boat commanded by the local crusader baron John of Ibelin, which was decorated with his own banners.
For the story about Richard and Leopold, see John Gillingham, Richard I (Yale University Press, 1999), pg. 224.