Avoiding all schisms? Ha! Totally ASB. All religions schism to some extent.
Avoiding the 'Catholic'/'Orthodox' split? Possible, but a touch difficult. You have to fix things on both sides for that to happen.
1) the Pope believed he had authority over the entire church, which no one outside his jurisdiction was willing to accept. If you have a much weaker Papacy willing to accept the 'primus inter pares' status, then that's one hurdle passed. But I'm not sure how to do that.
2) the Ecumenical Patriarch in Constantinople was effectively a minister of the Byzantine government. Ultimately, of course, as Bulgaria and the Russias became established as independent churches, the balance of power shifts some.
So.
As long as the WRE falls, the West will never accept dictation from an agent (even one just perceived so) of the Eastern Emperor. And no church in the East will accept dictation from the Pope.
I see a few ways around this.
1) The WRE never falls. The Church stays (largely) subject to the Imperium, which adjudicates squabbles between the Greek and Latin churches.
2) The ERE falls (or at least shrinks massively) much earlier than iOTL, leading to much earlier national churches. That still requires the Papacy to back down on the whole dictatorial power thing.
3) one of the cultures is totally devastated by foreign miscreant invaders (probably Islam). In that case, the tiny, barely surviving rump of one of the churches might be willing to be subsumed by the other.
4) Dueling papacies (akin to the Avignon split) happen much earlier, destroying the total authority of the 'Pope'.
Roman and Orthodox theologies are mildly different, but only mildly. The 'filioque' clause in the Western version of the Nicene Creed was a significant irritant, but was more a symptom than a real cause for division. The disputes on which pagan(!!) philosopher's version of reality best described the Eucharist is probably also workable around.
Other than that, it's pretty minimal. Lots of difference in practices, little in theology.