Yes, all those factors were involved. Even if they weren't the East and West would have split.
After the "fall" of "Old Rome" there was a political vacuum in Western Europe. In the chaos to follow any position of authority with some stability would be looked to for guidance. This sent a lot of political power to Rome.
In 756, Pepin the Short gave lands to the Roman See, which became the Papal States. This wasn't just a charitable gift given out of the goodness of Pepin's heart or his love for the Church. Pepin became recognized as the leader of all the Franks in return and Rome received help against the Lombards and Ravenna. As time went on, the Roman See became wealthy and the Roman See became more active as a political body and the Pope acted as a prince.
As JoeS mentioned, Charlemagne did have an immediate effect on the situation. When he was made emperor of an area that claimed to be a successor of the Roman Empire, the Byzantines became rather upset. The papacy was "married" to this new empire which was opposed by the Byzantine. Of course, at times, they weren't and the pope was fighting with the "Holy Roman Empire" for a long time after, so everything is complicated.
In the 10th century the activities of the popes started to become scandalous (see, for instance, http://www.newadvent.org/cathen/08426b.htm
). The papacy was a position of wealth and privilege and people wanted it for reasons other than spreading the Gospel.
Don't forget Photius and Pope Nicholas, the fact that practices were different (leavened vs. unleavened bread, etc.), Bulgaria, St. Gorazd, etc. etc. etc.
In reality it all boils down to whether or not you believe Rome has the absolute right to manage/interfere with all churches in the universe and whether or not the pope can speak with absolute infallibility on any subject, given the right formula (ex cathedra, although RCs can't seem to figure out what the heck that means). I know some will say that's extreme and that, as a practical matter, that's not what happens (I disagree). But this isn't about what someone practically does, it's what someone has the power and competence to do.
So, yes, they would have split anyway.