Only thing you really have to worry about is pesticides. A wild caught treat every now in then is fine, even if you're not sure how organic your yard is. If you live out in the country or are pretty confident your and your neighbor's yards are pretty poison free, it should be fine anytime. I would stick to months, butterflies, grasshoppers, etc. Stay away from wasps and bees, they seem to be controversial as feeders, plus they're more of a pain to catch, literally.
I've been feeding moths to my chams for years and love how much money I save when spring and summer come around. So far no deaths but then again I do live near the mountains where pesticides are used less often.