It is important to Jews, so we should be respectful about not using "Yahweh" when talking to them. But we can't take this too far. It should not be important to Orthodox Christians, because we are now living in the New Age of the Kingdom that has been ushered in by the Resurrection of Christ. Often people don't seem to get that. The non-use of the "Holy name" was one way of showing that humans could not approach the holiness of God. Another example of this is exhibited in the passage from Exodus, 33:18-23, where Moses is told that he cannot look God in the face and see his glory, but only His back, because no one can look on God and live. Well now we can, only because God has reached out to us in Christ and broken down the barriers between us. Wonder of wonders, we look at Christ and see God in the flesh! (This is not to say that the Holiness of God is still not a terrible and awesome thing; rest assured that it is!) Before Christ took on all of humanity to himself in Christ, divinization (theosis) was not possible. Now, we can "become" God, something that was inconceivable in Old Covenant times, and still is a scandalous idea to Jews today. This underlines, really, the fundamental incompatibility of Judaism (in its unfulfilled form) and Christianity. If we took the prohibition on utterance of the "sacred name" seriously, then the priest would not be able to say at the end of Vespers or Matins: "Christ our God the Existing One (or "He who is" or some variant, depending on the translation used) is blessed always, now and ever, and unto ages of ages" because it would cause terminal offence among the faithful! This is because "He who is" is the usage of the Tetragramatton (or I should say a variant of it) in whatever vernacular language the liturgical service happens to be in.
I sometimes have a tendency to beat an anti-judaizing drum on this board. This is because I believe that Orthodox Christians sometimes take parallels with Judaism too far, and this might be dangerous, obscuring important truths about the Faith. Christ is Risen! We are strangers to God no more. The Lord has made it possible for his children to come home once again. "Let no one weep for his iniquities, for pardon has shone forth from the grave. Let no one fear death, for the Saviour's death has set us free...(Hades) was embittered, for it was abolished. It was embittered, for it was mocked. It was embittered, for it was slain. It was embittered, for it was overthrown....It took a body, and met God face to face. It took earth, and encountered Heaven...Christ is risen, and life reigns. Christ is risen, and not one dead remains in the grave..." (from the Paschal homily of St. John Chrysostom.)