I think there are a few things going on here. First, while there's a great variety in the outward practices of many non-Protestant Christian Churches (e.g., the Greek Orthodox, Russian Orthodox, Roman Catholic, Coptic Christian, etc.), theologically the differences are actually fairly minor, and many of them are in communion with one another. So, for instance, the fact that the Russian and Greek Orthodox Churches are in communion with each other (or the Roman Catholic and Byzantine Catholic) means that both accept that the other is a valid expression of the Christian faith.

Now, of course, if you visit a Roman Catholic mass and a Byzantine Catholic liturgy, many aspects will be different (although there will also be many similarities). The churches will celebrate different feast days, they will fast on different days and in different manners, there will be different saints venerated, etc.

So does this mean that these traditions are arbitrary? I don't think so. How and when one fasts will vary, but the fact that one should fast does not. And the dates of a fast are not picked randomly --- in fact, if you look at any tradition of any of these churches, you will find very deep reasons for that particular tradition. It's just that there's not one right answer, so different churches have evolved their own unique answers (and in doing so, have emphasized slightly different aspects of the underlying theological truths).

So then why shouldn't a Roman Catholic like myself try out all the different churches until I find one that I like the best for myself? Living in a multicultural country like the United States, this part is harder to convey. But there is, I think, a great value in living in a society that practices its religion in a similar way. As an analogy, I could just decide that I would rather celebrate Thanksgiving on May 21 every year. But there's some value in living in a society where everyone, collectively, celebrates Thanksgiving on the same day so that families can get together and we can watch football and eat turkey. So while I could come up with my own way of practicing Christianity that would, in some sense, be valid, there is enormous value in accepting the traditions of my community that have evolved over centuries.

This all gets to a larger point in the Orthodox and Catholic faiths about hubris and respect for tradition. The idea is that, in general, practices don't stick around for centuries unless there's a good reason for it. You or I might not immediately understand what that reason is, but that doesn't mean that there isn't one. Moreover, and this is in contrast to many Protestant faiths, there is an idea in Catholicism and Orthodoxy that many truths come to us through Tradition rather than through Scripture. That is, Christ taught certain things to his Apostles, who taught them to the earliest Christians, who continued to pass them down the centuries. Some of these things were written down in Scripture, but not all. So, for instance, you won't find a passage in the Bible that forbids bishops from being married. But no Catholic or Orthodox bishops are married because this is a part of our tradition. But respect for tradition doesn't mean that the tradition is static. It just means that it changes only gradually and deliberately.