It must be a vocal minority rather than the majority of religious folk.
The official position of the Catholic church is anti-euthanasia; same with the Orthodox; Protestant churches vary but most are anti.
It's a case of a widening gulf between official church teaching and what the laity think. The same crops up in the usual culture war debates, e.g. homosexuality, abortion, etc. However, things could be changing as the pews are emptying and the resurgent churches are generally the ones who keep to a conservative line, and where the wider (increasingly young) laity agrees with this.
So these survey results will change over time.
