Well, before I launch into a long explanation, are there any particular instances you have in mind that I could try to address?

But without waiting for an answer to that, I'll try to give my own response. To fully cover the subject is book-worthy, so I'm going to concentrate on the first few centuries of church history. There have always been a variety of liturgies and worship practices within the Christian church - there has never been a time when there was one single liturgy and identical worship shared by all Christians everywhere. Nor do I think this was considered a problem; I can't recall any example of an early Church writer I've run across deploring such diversity.

But that's not to overstate the amount of variation between places. The general outline of the service has been remarkably consistent, from the earliest Apostolic era until the Reformation, and continuing today in the more liturgical traditions like Catholic, Orthodox, Anglican, or Lutheran. Details like which Psalms or hymns are sung in any particular service, or which Scripture texts are read, have had no single unified practice, but the overarching ritual of and content of hymns, Scripture readings, prayers, a sermon, and the celebration of the Eucharist have been standard.

Some of this was inherited from earlier Jewish synagogue practices, especially the first part of the service consisting of readings and prayers. This is seen even in the New Testament, in the book of Acts, as the apostles continue the Jewish practice of morning and evening prayers:

they devoted themselves to the teaching and the fellowship, to the breaking of bread and the prayers.

Acts 2:42, ESV. The phrasing in that passage, "the prayers" instead of "devoting themselves to prayer" has led some scholars to take it as more formal daily prayer services, not casual or individual prayers. Also, except for the addition of the New Testament texts as worship readings, the general pattern and the use of a lectionary system for rotating the appointed readings has been quite consistent with 1st century Jewish practice. The Eucharist, of course, is a uniquely Christian institution - while there are some similarities and theological connections made with the Passover meal, unlike that annual celebration the Eucharist was observed at least weekly in the early Church and came to be celebrated even more often than that. "The breaking of bread" in this Acts passage could refer to that, though it's not very clear.

Moving into the early Church, numerous writers offer information on the worship practice of their time and place, including the early 2nd century Didache, the works of Justin Martyr, Hippolytus of Rome, and the probably 4th century Apostolic Constitutions. Once again, these show agreement in the broad strokes but differing details.

One notable early reference to this diversity comes to us from Ambrose, Bishop of Milan, via the writings of Augustine of Hippo. He writes:

When my mother followed me to Milan, she found the Church there not fasting on Saturday. She began to be troubled, and to hesitate as to what she should do; upon which I, though not taking a personal interest then in such things, applied on her behalf to Ambrose, of most blessed memory, for his advice. He answered that he could not teach me anything but what he himself practised, because if he knew any better rule, he would observe it himself. When I supposed that he intended, on the ground of his authority alone, and without supporting it by any argument, to recommend us to give up fasting on Saturday, he followed me, and said: "When I visit Rome, I fast on Saturday; when I am here, I do not fast. On the same principle, do you observe the custom prevailing in whatever Church you come to, if you desire neither to give offense by your conduct, nor to find cause of offense in another's."^1

The attitude of Ambrose, at least, as a well-respected and prominent bishop of the late 4th century, was that such diversity in practice was no problem, and one should respect the local customs wherever they find themselves. Interestingly, this is probably the source of the saying "When in Rome, do as the Romans do." Ambrose wasn't free from such criticism himself, though. He introduced into Milan (part of the Western church tradition) certain melodies and chants from the Eastern churches, which prompted some to claim he was "bewitching" the people with the exotic music, though apparently the criticism wasn't strong or widespread enough to make any serious impact.

To speak to the other side, one issue that did spark real controversy was the date of the yearly celebration of Easter. Known today as the Quartodeciman controversy, in the late 2nd and early 3rd centuries the question under dispute was whether to celebrate Easter with relation to the date of Passover according to the Jewish (lunar) calendar (the 14th day of the month Nisan) regardless of the day of the week it fell on, or to celebrate it always on a Sunday as the day of the week when the Resurrection occurred. The date 14 Nisan is the source of the name, Quartodecimani, the "Fourteenthers". It seems that different areas practiced each through the 2nd century with little issue, but by the late 2nd century it became a dispute that ended with synods condemning the Quartodeciman practice and even excommunicating those who refused to align with the majority practice. Eusebius records:

A question of no small importance arose at that time. For the parishes of all Asia, as from an older tradition, held that the fourteenth day of the moon, on which day the Jews were commanded to sacrifice the lamb, should be observed as the feast of the Saviour’s passover. It was therefore necessary to end their fast on that day, whatever day of the week it should happen to be. But it was not the custom of the churches in the rest of the world to end it at this time, as they observed the practice which, from apostolic tradition, has prevailed to the present time, of terminating the fast on no other day than on that of the resurrection of our Saviour. Synods and assemblies of bishops were held on this account,and all, with one consent, through mutual correspondence drew up an ecclesiastical decree, that the mystery of the resurrection of the Lord should be celebrated on no other but the Lord’s day, and that we should observe the close of the paschal fast on this day only.^2

He goes on to explain that the question was not only the date of the observance but also the fasting associated with it. One of the Quartodecimans argued that they observed the exact date, "neither adding nor taking away", reminiscent of the language of Deuteronomy 4:2 to neither add nor take away from the Word of God. In that sense, regarding your initial question about justifying the claims as doing God's will, in at least this one case, it appears to be so. Still, it's interesting that here a question of fasting and feast date is worthy of excommunication, but a century later in Milan Ambrose suggests that local custom should be followed, and apparently numerous participants in the Quartodeciman controversy were of the same mind as Ambrose.

So while we have records of liturgical practice from different areas, we have little record of why such practices were chosen as opposed to others, and perhaps some contradictory evidence as to the overall willingness to accept diversity of practice. But I would certainly argue that the general trend has been diversity in details, unity in broad strokes.

Citations:

1. Augustine of Hippo, Letter 54 to Januarius, Nicene and Post-Nicene Fathers, series 1, vol. 1.

2. Eusebius, Church History, book 5, Nicene and Post-Nicene Fathers, series 2, vol. 1.

Other sources and further reading:

• Early Sources of the Liturgy, Lucien Deiss

• Springtime of the Liturgy, Lucien Deiss

• Liturgies of the Western Church, ed. Bard Thompson

• Christian Liturgy, Frank Senn