Questions about HRE, Rome and the Orthodox churches

I have reached a point in "Northumbria more successful?" where I can't ignore the power struggle between the Pope and the Holy Roman Emperors on one hand and between the Pope and the Eastern Patriarchs (especially Constantinople) on the other.
Now I have made the decision that in 1014 the western Church did not inserted the "filioque" phrase which removes one bone of contention and delays the schism of 1054 OTL(The Pope and Patriarch of Constantinople excommunicated each other!) but is the schism between Catholic and Orthodox churches inevitable?
Also is it inevitable that the Pope would win out over the Holy Roman Emperor in their dispute about who appoints the Archbishops etc.?
In both cases I mean given the political dynamics of the time which I haven't changed that much NOT that they would happen no matter what the circumstances.
 
Now I have made the decision that in 1014 the western Church did not inserted the "filioque" phrase which removes one bone of contention and delays the schism of 1054 OTL(The Pope and Patriarch of Constantinople excommunicated each other!) but is the schism between Catholic and Orthodox churches inevitable?

A schism of some sort is probably unavoidable, although the existence of a schism didn't prevent Byzantine/Papal co-operation against the Normans for the remainder of the eleventh century. To keep a schism from really going out of control, I'd suggest that keeping a viable Byzantine presence in Italy and Dalmatia is probably a good idea, complete with Latin-speaking Byzantine bishoprics in Apulia.

That's not to say East/West spats won't happen: they certainly will, and butterflying Manzikert and thus forcing the Byzantines to continue to deal, and attempt to compromise with, Armenian and Syrian Christian populations that they rule over will be as big a sticking point with Rome as it was in the sixth and seventh centuries. But the harmful effects of schism can perhaps be mitigated somewhat, and you can have a series of mini-schisms, punctuated by reconciliations and periods of grudging tolerance.
 
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