While I certainly do not mind listening to How Great Thou Art and Amazing Grace as sung by Elvis or other great gospel singers, I do not find that these songs have a place in the Catholic liturgy and intentionally do not sing them when played there.
Our rector is pretty serious about playing it 100 percent orthodox, we even use a missalette that isn't from OCP. Liturgical Press "Celebrating the Eucharist", with illustrations from the St. John's Bible (which is spectacular btw).
It's actually quite nice, good hymns in the back (largely German and older Anglican, with the usual older Catholic standbys (like "O Sacrament Most Holy"), and a few of the Eagles Wings/Gather Us In ones . . . but we just ignore those.)