I read it the way you do. Erm. And am lapsed protestant who went to catholic school. Not sure what that says. But I am surprised that "Some days, although we cannot pray, a prayer/utters itself. " is interpreted the way you say your students are reading it. I had never thought of the possibility that the people were praying 'even if subconsciously.' My interpretation is that the poem is about the inability to pray, and how the ritual sounds that are not actually prayers nonetheless offer comfort to these people who 'cannot pray.'
There doesn't seem to be an option for "some days, although we think we cannot pray, we do subconsciously anyway, and then noises sound like responses." That seems to be a bad-faith (sorry) reading, to me.