I, personally, do not find any compelling New Testament argument for Gentile Christians to participate in the areas that were understood to be ordinances, written by the hand of Moses (under the direction of God.) Acts 15 and many other New Testament citations seem too clear to me on that.

The early church struggled mightily over the question- "How Jewish does a Christian have to be?" In our age the question seems to have reversed itself- "How Jewish can a Christian be and still be a Christian?"

I personally see convincing evidence from the first generation of Jesus' followers that shares that they still had deference for the ten commandment law (both in teaching and in personal practice.)

I also find no compelling argument for New Testament Christians to ignore the issues of dietary concerns (the main reason why I've chosen to be a vegetarian- just because it's easier than worrying about Kosher issues in general.)

But, beyond that I personally have no particular agenda about whether or not you should or should not find some Christian growth in learning from those other rituals. In spite of the fact that most Christians hold that they were clearly given to look forward to the life and ministry of Jesus, I'll let the Holy Spirit bring you conviction in this arena.