Nathaniel Peters at First Things makes a case for Catholics singing Protestant hymns.
Because these hymns can be vehicles for handing on the Catholic faith, they remind us of the real meaning of Catholic. At its heart, to say that something is Catholic is not to say that it was written by a person in communion with the bishop of Rome but that it is in accord with the universal apostolic heritage. This means, of course, that not all hymns are suitable for Catholic liturgies. But it also means that if a hymn proclaims the Catholic faith, then—regardless of its origin—we should consider it a Catholic hymn.
This is the vision of catholicity put forward in Vatican II.
The whole essay is worth a read. You can find it here.