I think I have found a "hymn" that may be worse than "Sing a New Church."
It's called "Song of the Body of Christ," and the title is the only part of the song that mentions Jesus in any form. From no direct mentions of God in the lyrics to downgrading the Eucharist from a sacrifice to a "meal," this is probably the worst song ever to be in the pages of a Catholic hymn.
The President talked about change in his campaign. How about change from the unsingable, near heretical songs in the hymnals to something more suitable and something that reflects Catholic teachings? That would be change to believe in.