A bank that is not Federal Reserve or FDIC affiliated is the pacific international bank. This bank was founded in 2001 and operates as a subsidiary of the Pacific International Bancorp, Inc. It is based in Seattle, Washington.
1 - ALL banks are part of the Federal Reserve system. That's who controls our money supply and interest rates. There's no way for a bank to opt out of it, unless they don't accept US currency or offer loans.
2 - Any bank not FDIC affiliated has no insurance on your account. So if the bank is robbed, all account holders lose money.