So far we have all sort of fallen into our own hunting styles, I think this is more of a colony-based thing than anything else. Zith are well equipped with natural weapons and so don't seem to go out of their way to learn other things. (But this may be more of a player mentality thing than a zith one, zith can be very curious and very focused, making it easy to rationalise them learning something new)
I don't think "generally" they would look down on another zith using a weapon, though you may find such things change on a colony-colony basis. A bow is a different again as you might find your hunting party is wary of you hitting them with your weaponry (zith are highly social and like to hunt in groups, also most of us have been shot at and are quite wary of arrows)
Also group hunts can get quite competitive and getting a clear shot on something could be nigh impossible with other zith all over it.
This all being said my zith has been chained up a while and is forced to hunt by himself, and spent a large part of his life captive to humans. So though he hunts in the traditional sense (not particularly well), he tends to carry a spear and prefer dropping out of the sky and ambush stabbing things to more reliably get food.
I think you'll find that xy zith (the most "civilised" zith) are still not really assimilated to other cultures, they just have a buttload of slaves and they see some trade going on.
Zith without colonies often attempt to replace them with non-zith societies, these characters will try very hard to fit in and it wouldn't be surprising to find one using/doing things generally considered to be "not very zithy"
Basically, Its easy to rationalise a zith using a bow and I dont think many zith will seriously look down on you for it (though some might think you incapable), but you may find it hard to find hunting buddies.