I wondered. We have a yellow raspberry since this year and the chickens haven't touched itI grew them; two observations: 1. the birds don't recognize them as raspberries either, at least for a few years, so you've a better chance of harvesting them without nettingand 2. it's harder to tell when they're perfectly ripe than it is with the red ones.

The red berries are not tasty enough to fly into and getting gooseberries is probably too painfull. For the fruit trees they wait until the fruit falls (cherry, pear, apple, plum).