The Red Cross is a world-wide Non Faith-Based Charity. It is not run by a preacher who could help it understand the Will of Our Lord, but rather by a "Board of Directors" and an elected "Executive Director."
Although the group uses the symbol of Our Lord as its logo, that symbol is really nothing more than the flag of the pacifist cut-and-runner country of Switzerland where the organization is based.
To demonstrate just how far the Red Cross is from the kind of faithiness approved by Greatest President Ever, consider this: When it works in Muslim countries, Red Cross drops the Cross completely and calls itself Red Crescent.
The US Red Cross even gave Bill Clinton massive publicity after the Hurricane Katrina and the Indonesian Tsunami. It allowed him to act like he was a "good-will" ambassador.