According to this article at Mother Jones, Hilary Clinton is a member of a secretive but highly influential Christian political ministry, known variously as "The Fellowship Foundation" or "The Family," which, among other things, organizes the National Prayer Breakfast. All members of the Fellowship Foundation swear an oath of secrecy, ostensibly to prevent them from abusing their ties to the organization for the sake of public displays of faith.
Jeff Sharlet, an investigative journalist, has written an entire book on the Fellowship Foundation, and was interviewed about his research by Fresh Air's Terry Gross back in 2009. According to Sharlet, the Fellowship Foundation fetishizes power much more than Christian charity. They are also supporters of Christian fundamentalism in Uganda, including support for the strict anti-gay laws there.