I wholeheartedly agree that humans are invasive, but one need only look at a place like New Zealand to see how one of homo sapiens' most environmentally-damaging qualities is that it brings other invasive species with it. Treating birds at bird feeders as if they're all invasive is deeply reductive and objectively wrong. Animals migrate in some cases hundreds of miles in a day.
Cats are universally deeply invasive once feral, and humans letting those cats (and dogs) get out has been the primary threat to the wildlife of New Zealand. Not humanity itself. This is almost universally true on any island, from islands that have been completely taken over by rats, to the Spaniards' tendency to leave behind feral hogs that outcompete even the most deadly of predators within a couple generations. But in only one case does everyone treat this like it's some endearing quality: outdoor cats.
Just because there's a much bigger problem doesn't mean that the small one doesn't exist. That's just whataboutism. ALL of these need to be dealt with, but you know which one is the easiest to tackle FIRST? (Hint: it's not the pigs)