Looking back, obviously we consider it to be a pretty big deal, but were those involved aware of just what they were involved in, or was it mostly value assigned to that year after the fact?
Assuming the answer is no, at what point did people, in hindsight, start to point back o 1054 and say "that was it!"?
Additionally, assuming there were effects, whether immediate or drawn out, was this felt very much at the local level, or was it something that your parish priest would mostly have been ignorant about, and the impact mostly constrained to the higher levels of Church leadership?
I was taught that the value of the year 1054 was assigned long after the fact. The Great Schism was basically the finishing touch to a long period of widening distance between the patriarchs of Rome and Constantinople. For a long time after the fall of the Western Roman Empire, Rome remained under the sphere of influence of the Eastern Roman Empire and was therefore generally subservient to the Emperor (and his religious ideas). But as the Eastern Roman Empire's influence over Italy waned, the Papacy both saw its chance to dictate its own religious policies, while at the same time feeling suddenly threatened by other forces now that the Eastern Roman Empire no longer provided it with (limited) protection. In particular, the Lombards became more and more dangerous as time went on, and when Desiderius, the last Lombard king, managed to gain control of the two semi-independent Lombard duchies south of Rome (thereby effectively surrounding Rome with a unified Lombard territory), pope Adrian I called in Charlemange, who defeated the Lombards and placed himself as protector of Rome. Since then, the papacy was completely free from Eastern Roman influence and began to go its own way, both politically and religiously. The two 'sides' slowly moved away from each other, until eventually, the papacy was confident enough to begin expressing its ideas of Papal Supremacy to the Byzantines. Matters finally came to a head when two particularly headstrong religious leaders, Pope Leo IX and Patriarch of Constantinople Michael I Cerularius, decided to make an issue of the by now significant differences between Eastern and Western Christianity. They argued with each other, refused to compromise, and ended up excommunicating each other.
But that was basically it, there were no attempts by either side to 'spread' the conflict to the larger religious or political community, because, simply put, there was not a whole lot of intense contact going on between people of both regions. There was certainly no political consequence, no change in relations between Western and Eastern Christian states until the infamous Fourth Crusade in 1204 that ended up conquering Constantinople.