First of all, do me a favor: get down from your high horse. When someone writes: "it is said that...", it is usually a hint that the historicity of what comes after is somehow doubtful.
"(Odo of Mainz who fought in Italy with Barbarossa was notorious: it is said he fought with a mace, rather than a sword, to avoid spilling Christian blood)"
I honestly don't find any trace of hint on this tale being dubious. The use of "notorious" would possibly make me think first on "Everybody knows it was like that".
Now, if you say so, I trust you on it wasn't what you meant. But it's what it looked like. And honestly, it's really annoying to be regularly on this kind of pseudo-historical fairy tales.
Sorry if it was rude, though.
This said, legends and myths usually have a kernel of truth in them. Like the droit de seigneur, which most likely comes from the permission that serfs had to obtain to marry (and the tax they had to pay).
Or not. For the mace thing, it's probably came from a bad analysis of painting or writed sources without knowledge of context (as people that saw UFOs in byzantines painting by exemple).
The most exemple given is Bayeux Tapestry with Odo of Bayeux carrying a mace.
However, you have other people identified (or not identified at all) as nobles that carry such. That, plus the fact it was a long used symbol of power, would lead to the conclusion it wasn't probably a weapon.
Critically that, when you had actually fighting clerics, they used the same weapons than others. Adheymar du Puy using a sword by exemple.
Legends doesn't always come from a kernel of truth, but aslo because of bad interpretation.
Second, the emoticon was intended to show appreciation for the ingenuity in finding rationales to justify the circumvention of laws and rules, which applied to both ecclesiastical and lay laws. Ever heard of the "butter towers", for example?
The exemptions for eating restriced food weren't only used by churchs elites, but as well by nobles or even bourgeois elites. I don't see how it's a hint of how Clerics could have used maces.
It's just a proof that, in every era, elites didn't cared too much about moral legislation when they could compensate for legitimazing it.
Again, the thing is not about if Clerics or not actually fought (you had some), but if it was common and how it was, in order to manage to gave a POD where it comes to Popes making actual fighting.
The original ecclesiastical law prohibited all clerics to spill blood and to make war. The second part (making war) started to go down the drain almost at once (and certainly after the establishment of the Patrimonium Petri). Popes and bishops made war against heretics and infidels but also against fellow christians.
Making war =/= Fighting.
Unless we say Obama fought Taliban since 2008, for using a modern exemple. (Well, we could actually say that, but it would be abusive use of the word)
I don't see it more a circumvution than a feudal separation of powers.
They ordered reprisals and sent armies marching. In some cases they even led their armies (Cardinal Albornoz whom I mentioned for example) even if they normally did not participate in the actual fight. Why is this so disturbing for you?
It's not disturbing for me. I just try to answer the OP that ask for fighting popes. For answering that, it's better to search why FIRST they didn't fought but only organized armies and led them.
Now, again, you had exceptions : if figures as Albornoz are known, it's precisely because they were such.
Popes (and prince-bishops) were at the same time clerical and lay lords, and the two personas could be easily live in the same man.
Actually not.
Because clerical feudal worked a bit differently than secular ones.
While a secular noble could (and actually did) go to war himself, the religious one had to use a non-religious commander (I don't know the english word for "avoué", but that's ONE of the institutions avaible, with the possibility of making a neighbouring noble the protector of an abbey, by exemple, without giving him any feudal right on it).