Well it should ONLY be sung by those who are Quaker anyways, in their places of worship since that is its origins.
Sydney Carter's work is for secular performance - kind of like "Christian Rock" which doesn't belong in church either in my opinion (my husband the old rock guitarist says "It ain't Christian, and it sure as heck ain't Rock.") In the parish hall or at a youth meeting - go for it! (although 9 times out of 10 it's not music the actual youth like, it's music that makes the 60-somethings feel nostalgic for their youth.)
I'm always telling the story of the Worst Church Music Ever - in a Jesuit parish run by Franciscans (go figure) where the priest thought he could play guitar (he couldn't, couldn't even tune it - thought my husband was going to go over the pew and take it away and tune it). The rest of the "band" was a screechy lady of a certain age and an old gray-haired dude with a beard, ponytail and tambourine. And the priest's cellphone went off in his pocket . . . )