The obvious answer is, they don't. If you are a free-market fundamentalists then you are absolutely opposed to bank bailouts. That one is really really simple. See, the free-market means you leave the market to run itself. Bank bailouts involve taking taxpayer dollars and handing them to banks that would go belly up if left to the market. However simple this distinction might seem, it somehow escaped the NYT which discussed the policies promoted in recent decades as though they could be plausibly described as "free-market fundamentalism." It should be perfectly apparent to everyone at this point that the people designing economic policy in recent decades had no philosophical commitment to "free markets," they were trying to design policies that had the effect of redistributing income upwards. In the case of the banks this meant giving them implicit government insurance, both through the FDIC and the "too big to fail" policy, without constraints on their behavior or making them pay for it. This approach has nothing to do with free markets, it is a story of wealthy people using their political power to get valuable benefits from the government. The NYT is insulting its readers by implying that these policies had anything to do with free market philosophy.
--Dean Baker
