The mutual excommunications and heated polemic of the 1050s make for dramatic history-telling. But in the scheme of Greek-Latin relations, 1054 as a watershed year of Schism is really more of a modern convenience to say, "Yeah, by this point East and West had grown far enough apart to be different churches."

The key here is grown. This schism was not a question of a new claimant to a Church office or a new interpretation of theology or a new religious practice. "Catholicism" and "[Greek] Orthodoxy" are simply the labels put on the systems of practice/belief that had evolved within the Latin and Greek-speaking Christian churches.

So the 11C schism wasn't a matter of individuals choosing one belief/praxis system over another. It was, more than anything, a matter of continuing to go with the previous flow of one's area/church. For the most part, people in the West would have known only Latin Christianity, and people in the East, only Greek Christianity. There really isn't a question for them.

We do know of some cases of Greek churches in Latin areas and vice versa. However, even in these cases it is unlikely that families would have been split, i.e. that one son and his wife attend a Greek church in Ravenna and the other son and his wife go to a Latin one. First, noble families developed patterns of patronage and allegiance to particular churches and monasteries. Second, you would have grown up in one church's particular style of Mass and and worship, and been accustomed to it. (More to the point than Mass, I think, is veneration of icons, as that would be a daily practice that would differ to some extent between East and West. I am thinking here of the nobility rather than dirt-poor peasants--we have a lot of evidence of "pious noblewomen" in particular who would have grown up praying with the aid of images vs praying and venerating images.) Third, it is possible that language affinity might have been a factor for some people.

But more to the point here, perhaps, is that the schism would have reunited families with members attending different-Rite churches, rather than dividing them. The antagonism of the 1050s was heightened by Latins' closure of Greek churches in Italy, and the Greeks' closure of Latin churches in Constantinople. That would have put anyone who wished to worship in the building and Mass of the locally-dominant church.

There is also the question of just how much lay people knew about religion in the mid-11C. My knowledge of Byzantine catechesis and pastoral care is basically nonexistent. But I can say that in the West, we absolutely have some signs of lay people taking a very vested interest in religion and religious belief/praxis at this time. However, it is not at the level of, is the bread for the Eucharist leavened or unleavened (a central theological debate of the Schism). In fact, it is not until 1215 that the Latin Church will mandate lay people receive the Eucharist at all! Would they have been able to tell, from the back of St. Maria Maggiore, exactly what the priest was holding in his hands? (If they were in church at all.)

And one final point concerns the importance of family. Five hundred years later, Martin Luther himself will tell newly-Protestant women who find themselves married to men loyal to the Catholic Church that their marriages must override their religious beliefs. 1550 is not 1050, of course, and the Church's greater attention to the laity in the late Middle Ages means that they also paid a lot more attention to the importance of family, in general, in 1500 than in 1000. But betraying or splitting one's family in the premodern world was not something lightly done. Even with salvation potentially at stake.

So for a variety of reasons: historiographical, ecclesiastical, geographic, pastoral, the Latin/Greek divergence in the 11th century would not have split families. And indeed, it only sort of splintered Christendom. Less than fifty years later, Western Christians rallied in part to support the Greek emperor. After the (Latin) Normans conquered Sicily from the (Muslim) Kalbids in the late 11C, Greek Christianity on the island enjoyed a resurgence with Latin support. Although the Crusader Kingdom of Cyprus in the later Middle Ages established itself as a Latin superiority over a Greek majority, Church art and architecture during that era suggests a good amount of religious, even theological exchange--possibly even showing that Greeks and Latins were worshipping in each other's churches. (Not to mention the situation in the Ottoman Empire, where Christians rotated use of whatever church building existed.) Delegates from the two Churches continued to meet throughout the Middle Ages to attempt to resolve their theological differences and reunite. Neither the Latin nor the Greek Church made any such attempt to reconcile with Arians, Nestorians, Donatists, or any number of groups they declared heretical.