all migratory birds are protected. that said, i shot my share as a youngster. we had a cherry orchard and they would line up on the power lines. as soon as one dropped, another would take it's place. a 200 bird day was typical. now, as an adult. i just shoot starlings and sparrows.
yes grackles are loud and will keep songbirds from feeding, but i've found if i place a large quantity of cracked corn away from the other feeders, they'll eat that instead and cracked corn is only $6 for 40lbs.
i've also seen 1 bluejay scare away a dozen or so grackles, so i place a tin of whole corn near the feeders for the jays.