In the Catholic Church, the change began last century as a result of the directive of Pope Pius XII (Divino Afflante Spiritu) and the decree of the Second Vatican Council (Dei Verbum) that new vernacular Bibles be produced in which translational preference should be given to the original language texts. In the case of Psalm 23, that meant translational preference was to be given to the original Hebrew text. Previously, in the English Douay-Rheims Bible translational preference was given to St. Jerome’s Latin Vulgate over the Hebrew, which in turn appears to have given translational preference to the Greek Septuagint over the Hebrew. The Greek Septuagint was the pre-Christian translation of the original Hebrew texts favored by the first Christians. The authors of the New Testament itself gave translational preference to the Greek Septuagint over the Hebrew.
Protestant churches began giving translational preference to the original texts much earlier. The 1611 Protestant King James Bible reads, “The Lord is my shepherd.”