It is illegal for them (or anyone else, for that matter) to refuse you service on the basis you choose not to give your SSN.
I know someone who sued Walmart for $10G when they refused to cash a Walmart money order (or cheque) because they refused him service for not disclosing his SSN.
The SSN is a private document that needs to be kept secret from absolutely everyone. It even says that of the card itself!!
Not sure where you are getting that from. Amazon, like ******, is being required by the IRS to record transactions so that sellers can be taxed on income. I would check their guidelines, but ****** only has to report to the IRS if you have over 200 transactions and $20,000 in volume. Sounds like you need to use Western Union or MoneyGram if you don't like their new guidelines.
But honestly, while ****** can be a pain in the ass sometimes, they are offering a service for both buyers and sellers and I think it's only reasonable for them to take a cut of that. They aren't in the business of processing transactions for free. You pay for the convenience of getting money instantly.