Do they know that guitars come from the middle eastern region? Which means that, by their extreme kind of logic, any music involving guitar is middle eastern by origin, and by extension, 'heathen'? If I were you (if you're not getting paid to do play) I would do what I want. And do my best at it.
Well Christianity itself is middle eastern in origin so none of that (what you're saying *or* what you're saying "they" are saying) makes any sense.
