If they cold-contact you, it is not rude to simply ignore them.

If you have an existing relationship with them, then it could be considered rude, but it would depend on your relationship.

I replied to a first follow up (~'I don't think I'm a good fit', nevermind anything else) this morning as it happens. Almost always ignore; took one as far as interview a few years ago, which I never heard back from (no result/feedback) until a week or so ago! But I might make that a policy, if they 'just check in' after the first email then may as well try to head it off there I suppose.

I can tell Amazon isn't banging down your door. Seriously, it's insane how no one at Amazon Recruiting talks to anyone else in Amazon Recruiting.

They're all cold emailing you with a canned email. It's about as close to automated as possible.

In most cases they use automatic follow-up systems and if you answered then the system will stop automatically route to you next e-mails.