I sometimes call the Jays, "Picky Petes". :D We've caught many birds in our live trap, but never a Jay.
I used to think Jays were bullies, but then we got Red-bellied Woodpeckers. We are in such a habitat that we have Western Meadowlarks year-round and some have actually braved going to a platform feeder to get peanuts. A Red-belly did NOT like that and tried bullying the WEME. The Meadowlark would take none of that which confused the woodpecker.