Earwigs can run quite quickly, so that would suggest that they are 'hunters' rather than vegetarians! They do in fact like a feast of aphids, so might not be totally accepted as a garden pest. Much depends upon your tolerance level of things creepy-crawly!
The main damage caused to plant by Earwigs, is small holes in foliage and flowers of some plants. Dahlias and Chrysanthemums in particular. The type of flowers associated with these plants, makes for a good hiding place for the long bodied insects. Earwigs have a nasty habit of dropping out of cut flower arrangements!
Affected blooms will have ragged edges where the Earwigs supplement their aphid meal with a 'veggie' course - not good for those wishing to grow prize blooms.
Badly affected plants and greenhouse areas can be sprayed with Bifenthrin, or you can tap the stems of the affected plants and 'collect' the insects that fall out - very effective with dahlias and Chrysanthemums. Another 'organic' way is to leave a few upturned pots about - filled with straw old screwed up newspaper and leave around as traps for the Earwigs. Having caught the Earwigs, you can then 'dispose' according to your squeamishness or degree of sympathy you have for other living creatures!
Earwigs normally feed at night.