One of the several sects of Christianity I explored before going to the Episcopal church was Messianic Judaism, which is mostly of a Protestant flavor; I bought The Complete Jewish Bible which, although not totally accurate in its assumptions, did indeed allow me to appreciate the Jewishness of the New Testament (we often forget how the NT was written and read with Jewish eyes - NT Wright reminds us that we need to remember that when we read its message). In the CJB, they would not dare use the Lord's name and often you saw Adonai in its place; this must be what helped cement my feelings about this subject, not that those who use YHWH are somehow wrong or not good Christians - it's just that I personally didn't feel comfortable with saying the Name.
The Holy Ghost must have been moving many at the same time because shortly after I became a Catholic, the Vatican announced in 2008 that Catholics should not use YHWH in our hymns, liturgy, or prayers anymore. Francis Cardinal Arinze, by request of then-Pope Benedict XVI, wrote a letter explaining the reasons behind this request. The US Conference of Catholic Bishops released a copy of this letter and welcomed the clarification by Rome, "as it helps to emphasize the theological accuracy of our language and appropriate reverence for the Name of God so consistent in our tradition." Of course, SOME fundamentalists (who never do any research) started shouting that the Vatican was "denouncing" the Name of God. You can't please everyone.