Can envy happen between denominations/belief systems, etc.>
I suspect that with protestants, if you envy another church you can always go and join it.
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If you define envy as resenting the virtues, the good reputation, prosperity, and success of another---and wishing they would be taken down a notch or two --- then sure, it happens all the time between denominations. Of course feeling steamed about some other church enjoying growth or influence or success, is still the sin of envy.
Envy shouldn't be confused with emulation, which is recognizing another person's or group's excellent qualities, and being spurred to be more like them. Like, "Dang, those Baptists sure can quote chapter and verse! I wish more of us Catholics could do the same. Maybe I should really take a Bible course."
Didn't St. Paul say something somewhere about trying to out-do each other in virtue? (C'mon, Baptist friends, help me out here...)