By what I’ve read, this feud was extremely bloody and almost personal, with the pope wishing to destroy the Hohenstaufen bloodline. How did others perceive this (in hindsight) obvious perversion of the crusade ideals? Were they worried about papal overreach? Does this feud in any way tie into the end of the crusader era?
In short, the event in 1239 itself probably looked not so unprecedented change of tide for the contemporary observers, mainly on the following backgrounds:
It was also not just tyrant (?) lord Markward that Innocent tried to fight under the banner of crusading - he and Latin Christendom had another possibly problematic/ marginal groups of self-claiming religious people, sometimes labeled as "heretics". Innocent defined the heresy as a public crime, treason against the papal authority, and further, justified the use of arm to suppress their possible threat. Later Innocent also applied this legal theory to the field by initiating the Albigensian Crusade in southern France (1209-29). Rist also suggests that Innocent kept in mind that the letter of calling for the crusade against Markward was also to be read by crusade preachers (Rist 2009: 195).
In the famous circular letter addressed to rulers and princes across Europe, Pope Gregory calls Emperor Frederick as a heretic as well as contemptus clavium (the man who denigns the papal authority, symbolized by the key [to the heaven, conferred by Jesus to Apostle Peter]) (Althoff 2013: 210-12). According to Pope's rhetoric, Emperor Frederick was a traitor to the papal authority, thus the crusade against "heretical" (in fact, disobedient) emperor should be justified also by the legal foundation that his predecessor Pope Innocent III had already formulated.
What might be unprecedented was Frederick's very swift response - his chancery also wrote a circular letter that accused the Pope and justify the action of the emperor, also addressed to rulers and princes across Europe. This propaganda war between the Pope and the Emperor, however, might also have been an echo of more than 150 years ago - Pope Gregory VII and King (not yet Emperor) Henry IV of Germany as well as their supporters on both side had also circulated letters on "the first public sphere" in Latin West.
A few contemporary authors could indeed observe the situation without affected by the propaganda from either side - to give an example, English chronicler Matthew Paris makes a note that the conflict on the lordship on Sardinia was a real short-term issue at stake between Emperor Frederick and Pope Gregory (Rader 2013: 448f.).
A far more impactful event for whole Europe than their conflict, however, would soon broke out - Popes would also have to consider the possibility of calling for the crusade against the Mongols after their Great Invasion (1236/37-42).
Thus, we should perhaps consider the significance of the conflict between Frederick and Popes from more longer time spans, as Rist concludes:
"Due to the decisions of popes between 1198
1189and 1245 to authorize 'internal' crusades, by 1245 popes had a greatly expanded idea of the uses to which crusading might be put and this influenced both clerical and lay views of crusading......
By 1245 the papacy had a much broader concept of the uses to which crusades could be put - which impacted on the concept of crusading itself. The die was cast: it was the 'political crusade' that would dominate the explosive politics of Dante and Petrarch's Italy from 1250 to 1400 (Rist 2009: 226f.).
Cited References:
(Edited): fixes typo.