This is a tired old flawed argument. I'm not going to bother.

Judging by the horrendous effects of climate change, I’d say humans deserve that classification more than cats do. I thought habitat destruction was a major cause of damage to wildlife. Cats aren’t doing it.

We are surrounded with Invasive Alien Species. Even if they are, I think they're tremendously cute anyway!

I have to agree that cats are aliens, but they are not an Invasive species as they only further the strong to live forward. We have six cats and will probably get more, they are just to cute not to love and hold and scratch.
As to their being aliens, I have it on good authority that they are from another world and are here to assure the furthering of our species, that is if we will pay attention to them.

Most pet cats are never allowed outdoors anyway, as it shortens their lifespan and is hazardous to them, so classifying the whole group as dangerous to birds and other wildlife is wrong...

I happen to agree. Cats that are kept indoors live longer, don't procreate, don't fight, don't get exposed to diseases, are cleaner. Some cats will wear a harness and can be safely taken outside. The fleas here are so bad mine are indoors only.

Same thing with the feral horses that are overgrazing the west. Both are introduced species, it does not address whether they are desirable or lovable, it merely states they are alien to their current environment.

Like it or not, nature is nature.