I found out that William of Normandy's brother, a bishop fought at Hastings with a club. This made me wonder how involved the clergy got when the Christian Kingdoms were invading each other. I was thinking more along the lines of direct military assistance, because I'm aware the Pope often wrote letters to try and end wars if they likely to interfere with planned crusades or other events the Church planned.
Clerics are canonically forbidden from the shedding of blood, and could be excommunicated for doing so. However, there is a popular motif of the warrior-bishop, most evident in the crusading epic La chanson de Roland, based on the Battle of Roncevaux in 778. Bishops were often temporal lords, and how often they might ride into battle, particularly in the period of very loose papal control ca. 850-1000, is hard to say.
The Church itself was firmly against inter-christian warfare, a stance which is evident in both the Peace and Truce of God movements. Crusades (and later, the militant orders) were encouraged as a healthy and salvific alternative to this sort of war.
So, as with most things, the picture is muddled, and high pronouncements of canonical regulation were sometimes disregarded, but also sometimes followed.