The best way to handle this is by using bird nests, which are way safer than messing with those screechers trust me. First, you'll want to get some palm leaves planks and giant clams together, and once you've researched the nest at your table you can start crafting them. Something interesting about this whole setup is that the seagulls are actually pretty skittish, so try placing your nests in the quiet corners of your raft or maybe up on platforms where you don't walk around much.

Give the nests about 30 minutes between checks, and you should find around 3 feathers in each one if you're lucky. The birds get spooked pretty easily, so try not to hang around the nests too much while they're doing their thing. Sure, those screechers drop feathers too but they're seriously dangerous and not worth the hassle when you can just let the seagulls do all the work for you.

This setup might take a bit to get going, but once you've got a few nests running it's basically free feathers without any of the risky stuff that comes with hunting.