If it's just that you might as well just ignore it and not cause any additional noise.

Not GP but I can’t shake that it feels rude, even if expected.

But more practically: if I decline after the first, I don’t get the other 4 emails they have queued up for me

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 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.

I’ve gotten two messages from internal Amazon Retail recruiters via LinkedIn about “exciting opportunities” over the past year.

My LinkedIn profile clearly shows I work at AWS…

I've started getting very firm with them. I respond to each email with "no thank you, also stop contacting me, also here's the last person I asked to stop contacting me, but who didn't." We'll see how long it works, if at all, but after 3 separate Amazon recruiters contacted me last month I was fed up.

Amazon is getting ridiculous. I get an email from them almost every day

Just wait till you get a cold text from them.

For me: Linkedin inmail->email->cold text within 3 minutes.

When I told the guy that was pretty unprofessional. His response "it's just text mate".

Escalated to jeff at amazon. That got his attention pretty quickly.

I still get recruiters trying to recruit me to amazon.

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.

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.

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