In the 1960s, ethnomusicologist George Pullen Jackson recorded Amish hymns in Lancaster. With permission (not everyone's). Recordings exist — in Smithsonian archives.
Reaction
Mixed. Some communities: 'Why record a prayer? Prayer is alive.' Others: 'Let them record — maybe someone will hear and think.' Still others: 'We don't care' (pure Gelassenheit).
YouTube
Now you can find Amish singing on YouTube. Filmed by tourists. From a distance. Bad audio. But even through a phone speaker — you hear: this isn't music in the usual sense. It's prayer that sounds.