Just curious, where does Amazing Grace divert from Catholic doctrine?
Wherever it is, it's a lot less heretical than some supposedly "Catholic hymns" that appear in Catholic hymnals.
The argument that I saw objecting to "Amazing Grace" seemed to mostly object to the line "How precious did that grace appear, the hour I first believed", assuming that it left no place for grace to be received through the sacraments, but only "the hour I first believed". But it doesn't say "I received the full plenitude of grace, the hour I first believed," but only "how precious did that grace appear".
I thought the argument was rather specious. As I say, there are far worse "hymns" foisted on the Catholic faithful.
For instance we do not say God's grace is dependent upon belief, but dependent upon God alone. Others could interpret differently