Not much macrohistoricaly
For a simple starter, this means no First Crusade, or at least making it less likely.
I find that far from obvious.
Crusades were possible thanks to a social/ideological evolution and integration of
miles* into a Christian way-of-life : If violence against Christians from a class whom whole legitimacy was based on warfare was frowned upon, the logical outcome for milites, in order to be religiously legitimized, was to use this violence to serve Christians.
Legitimisation of violence, especially from a military-based social class (less nobility as a whole strictly speaking than milites, aka warring nobility), that was in the direct continuation of Truce of God and XIth councils played an important role : it did help that Urban II was issued from this nobility, and most able to speak to them, calling to their own conceptions.
True, the concept of Crusade as we know it could possibly emerge differently, but I don't see any good reason why the simple absence of Urban II would butterfly it except as a "PoD => Random **** happens" equation.
But how else is history changed if we don't see the Gregorian Reforms during this period -- reinforcing clerical celibacy, reforming the calendar, marriage...?
Similarily, I don't see how you would really escape the reforms, even if they wouldn't be called Gregorians.
The re-organisation of the church along Roman lines was not only far from a novelty (altough it certainly carved the face of classical medieval Church), but most of its contents not as much comes from Gregorius' own conception, than being already widespread in episcolap and monastic centers of western Christiendom already. The lesser feudalisation of clergy, for instance, was already well opposed by the Clunisian structures.
The whole program of rejunevation was already carried by Leo IX and Nicolae II, before Gregorius let its mark on it : I don't see a good reason why another candidate would suddenly give up this. You'd argue that the Dictatus was a relativelty radical affirmation of pontifical autonomy and power, and honestly that would be true and the face for the reforms could be significantly changed.
But as much the empire and the italian potentes could push back and modify the most radical elements of the reforms, they couldn't get rid of it. Not only because there was a general push for a rejuvenated church even from aristocracy, but because even the emperor benefited from a better legitimacy for his own authority from a more independent church (more independent church, NOT fully independent church) from aristocracy.
And what else of the more immediate political effects -- would this mean, under Henry IV, that the Holy Roman Empire might become more centralized?
Mostly coping from another thread : the imperial character of medieval Germany and Italy was an issue there. These existed as cultural, political and proto-national ensemble, but the overlording body was the Empire. It led the various strong dynasties to live up to their quasi-universal pretentions if they wanted to legitimize their rule. It led to clashes with Papacy, itself quite bound on universal hegemony, and the various city-states, duchies, etc. that could benefit from the big extension of the Empire (HREmperors could be forced to end a revolt in Italy, mere years after having dealt with Germany) and from pontifical support (HRE, too far from God, too close to the pontiff).
And there's the kicker : while other kings and great nobles didn't THAT feel threatened trough excommunication (they still did a bit, sometimes), HREmperors did. They needed the pontifical aquescit to legitimize their rule as emperors, and excommunication didn't just meant for them that Rome was very, very, disappointed. It meant they were theoritically deprived to their right to rule as emperors, which litterally everyone could use as a pretext to revolt : the strong papacy Ottonian supported at first in order to legitimize their imperial claims became more and more of an hinderance.
Full disclosure -- I am seeing this as partly being
an effect of Godwinson winning at Hastings, and for that matter, as part of
a larger TL.
I'm not really seeing why. The importance of pontifical influence on the conquest was vastly overrated, if not more or less forged in Modern Times.
