By "fighting churchmen" I mean ministers like priests/bishops, monks, and friars who took active roles (i.e. fighting and killing) in battles. I know there were monastic orders of knights like the Hospitallers and Teutonic Order so I'm not asking about those (correct me if I'm wrong but my understanding is most of the actual fighters in those orders were laymen anyway).
And yes, I know "Medieval Europe" encompasses a lot of people, places, and wars over a long stretch of time so if the experts wish to speak specifically on one or two times and places that's fine, or just a general overview is fine too.
In Spring 1218, an Oeselian army, a pagan people of the Baltic, marched upon the Christian settlements in Metsepole, a region in Latvia. A parish priest, Godfrey, mounted his horse and rode to the surrounding villages, summoning help from the German bishop of Riga. The next day, the Christians faced the pagans in battle:
"There were only seven of the servants of the German bishop and the eighth was the priest Godfrey, who belted on his weapons for war and put on his breastplate, like a giant, desiring to save his sheep from the jaws of the wolves. They rushed valiantly upon the Oeselians from behind, killing some of them most bravely."
This account is taken from the chronicle of Henry of Livonia, himself a parish priest. Clerical armsbearing certainly did happen though it is difficult to state exactly how common it was. Canon law had repeatedly condemned clerical violence in the eleventh century. From 1049 to 1079 twelve church councils or synods, seven under the direct auspices of the papacy, forbade clerical armsbearing in some form, suggesting it was relatively common, or at least the church thought it was. However, by the late medieval period this opposition had shifted. The advent of the crusades, military orders like the Knights Templar, and new developments in just war theory all contributed to more lax rules on clerical violence as did the conclusion that by natural law priests had the right to defend themselves. A late fourteenth century canon lawyer in Bologna, Giovanni da Legnano, assessed a series of instances to decide when it was acceptable in canon law for priests to fight and kill. These scenarios included:
Answer: yes, but only if the child will survive the time it takes to kill your attacker. Otherwise you need to baptise them whilst you're being murdered.
Answer: Yes, but only if you are in mortal danger and there was no other way to defend yourself and continue the mass.
After the eleventh century clerical violence was no longer repeatedly condemned as it had been. Of the seven ecumenical councils from 1123 to 1311, five did not mention the matter at all. When armsbearing was condemned, it often seemed contradictory, as at the council of Vienne in 1311-2. The same council ordered that Benedictines could not bear arms in their abbey precinct without the permission of their abbot, suggesting that they could bear arms outside. In 1289, Nicholas IV allowed the Franciscans to carry weapons 'in defence of the Roman Church, the Christian faith, or their country, or with the permission of their ministers'.
Senior clergy were sometimes freed from restrictions on armsbearing. The Carolingians tacitly exempted bishops and abbots from the definition of 'clericus', allowing them to serve militarily. The 1050 council of Coyanza ruled that priests and deacons in the Castillian diocese of Oviedo, were barred from 'arms of war'. Bishops were not mentioned, possibly deliberately as such senior ecclesiastics could often be found serving as royal commanders. For example, Anthony Bek, bishop of Durham, was with Edward I when he put down a Welsh uprising in 1295, participated in the English invasion of Scotland in 1296, and fought at the Battle of Falkirk in 1298. In 1300 he besieged and stormed his own cathedral of Durham following a dispute with the prior over the right of visitation. An anonymous poem of the event recounts that:
"From boyhood Bishop Anthony
Had learned to fight most readily,
And in violence trusted more
Than in the texts of canon law"
But such violence was not universally condemned. The Pope made Bek patriarch of Jerusalem in 1306. When he died in 1311 Bek was buried in the same cathedral he stormed and whose monks he attacked. He became the first bishop of Durham since St Cuthbert to be buried there.
It is likely that frontier areas like Livonia and the Crusader States were where clerical violence was most common and perhaps the most tolerated. In 1119 Bernard, patriarch of Antioch, defended the city with a force of 'armed clergy and knights' until Baldwin II of Jerusalem arrived with a relieving force. In January 1120 a church council at Nablus, held by Baldwin II and the patriarch of Jerusalem, allowed clergy to bear arms for defence.
Henry of Livonia's chronicle has several instances suggesting that priests in the Baltic had to be prepared to fight at short notice. The passage above states that Godfrey's weapons and breastplate are 'his', suggesting that this parish priest had his own weaponry and armour. Henry also appears to have approved of Godfrey's actions. 'like a giant, desiring to save his sheep from the jaws of the wolves' are references to passages from Maccabees and elsewhere in the Bible.
Another passage describes an attack by the pagan Kurs on Riga:
"The citizens, the Brothers of the Militia [the Sword Brethren], and the ballistarii, few though they were, together with the clerics and the women, all had recourse to arms"
Henry even mentions an anecdote featuring himself ready to fight. He and his fellow priests were interrupted whilst baptising a man called Kyriawan:
"While we were on the point of annointing him with the holy oil, a great clamour arose and a rushing of our army through all the streets and everyone ran to arms, crying that a great host of pagans was coming against us. We immediately put down the holy chrism and the other holy articles, therefore, and hurried to the ministry of shields and swords."
Sources:
James A. Brundage, The Chronicle of Henry of Livonia (Chichester, 2003).
Lawrence Duggan, Armsbearing and the Clergy in the History and Canon Law of Western Christianity (Woodbridge, 2013).
T. E. Holland and F. W. Kelsey (eds), Tractatus de bello, de represaliis et de duello (Oxford, 1917).