Unusually for me, I'm on the fence here as my local cats help suppress the invasive alien Brown Rats, so they are moderately welcome in my garden. (I was definitely tickled when Dolly the tabby dumped one on the glass roof of a neighbour's conservatory.)
I don't actually feed the birds but they find a lot of insects and as far as I can tell woof down a lot of Buddleia seed. The Blackbirds like the Holly berries. I keep the ground-level cover to an absolute minimum including trimming off low branches, so ambushing birds is pretty difficult. Hopefully difficult enough: I've never seen any of the cats catch a bird in my garden.