The Federal Money Market Fund is approximately as safe as FDIC. At the end of the day it does have its pricing set by the market, so is <not guaranteed to be perfectly stable, though it has been so far>. Even a FDIC bank may not be able to guarantee money will not be frozen ever for even a day, which is equivalent. The Federal Reserve and Treasury have an extreme interest in maintaining the perfect stability and liquidity of their short term debt at all times and will do literally anything in their power to make that happen. Federal Money Market, Federal Deposit Insurance, guess who is behind both of those...
Often FDIC savings accounts have better yields.