How DO I open a bank account that is not attached to any SS number or State ID?

[allodial]

Corrected. TYVM.

People do it everyday. http://jesse2012.com/signcard.jpg
Looking closely you'll see the "Under penalties of perjury, I certify that..." language is straight from the IRS Form W-9.
Bank of America does not hide it, Substitute Form W-9: http://jesse2012.com/BAsigncard.jpg

These signature agreements are examples of an easy way to quickly establish a lawful money bank account for the person with the SSN. The person has the SSN, not me. But I use the account for my benefit. Works great for direct deposits and has not hindered my 8 year success as a NONtaxpayer.

If you'd like to establish a bank account without SSN using Form W-8BEN, you should seek out Michael Joseph. He's the goto guy for this. You may want a good grasp of trust law to get 'r done.

As was much discussed on the older sites (2000 to 20010), one can file a fictitious reg with the SoS or County Clerk or something like that showing John Henry of the private household called "Smith" near Lallapalooza, Tennessee doing business as JOHN SMITH, 100 Main St., Memphis, TN 00000 or the like. One could even obtain an EIN and bring both fictitious registration and the IRS EIN assignment to the bank. Perhaps alternatives might come to mind.