Perhaps it is regional. Where I grew up the error-repair gesture varied certainly (forehead, lips, etc.) but I went to Catholic school for a while and I do not recall the distinction being neatly by religion but my memory isn’t that sharp of that period of my childhood.

Considering the rationale offered by Hindus, I’d be inclined to believe it is a Hindu custom adopted by everyone else by virtue of relative numbers. Sort of like how Christmas is secular in the US, Diwali in India, and perhaps weaker something like Eid in Jordan.

So I agree, very little to do with religion today, but perhaps not so always. Something like Halloween perhaps.