If no marshals were aboard the plane, it would strictly be the captain's word.
Hardly. Not when an entire aircraft-load of passengers heard what he said!!!
WestWind1950 ... that would have been my first thought too. I would not have felt comfortable with being asked to publicly identify myself for ANY reason let alone on religious grounds and I would not have felt terribly happy at the prospect of remaining on board after that ill-advised announcement.
What the pilot did was inexcusable. An employee on company time should not indulge in personal crusades.