Generally speaking, I think Ann's response on spiritual issues is rather different to her response on moral/ethical issues. I mean, there's Nicola looking at her with surprise as she appears "gay and recollected" on returning from church. Her response to Edward Oeschsli, however, is very much a "render unto Caesar" approach (and while it's perfectly valid that the rest of the Marlows utterly disregard the human aspect when it manifests in the person of Judity, Ann disregards Edward and Felix's human aspect also).

Where Ann comes over as thoroughly unsympathetic is the reason why she refuses to lend her bicycle to Nicola, though. That one is narrow-minded (if I'd been Ann, I'd have never lent my bicycle to another family member for different reasons, but the reason given is obnoxious). Basically she's putting obstacles in the way of Nicola's spiritual journey because she's being sectarian about things.