eas7888, I see your point in that they are a humanitarian organization and to remain impartial etc. etc. However the rub comes from being a member of the forces actively engaged in a war against them. By contributing to the organization you would be in part personally supporting free aid to the enemy. Aid which enables them to return to the fight, plant more IEDs and harm other fellow soldiers. I would not give up a pint of blood for it to be pumped into an insurgent so that a month from now he can shoot me in the head on TV. I understand that is a highly unlikely extreme, but the point remains. I have to agree with fc2spyguy.
Let them be humanitarian and support whomever they chose, but not supported by me.