As far as Islam is concerned, there is nothing wrong in offering charitable work that aims at helping the needy and the oppressed. Islam encourages all efforts that aim at bettering the situation of people and alleviating their suffering.
There is a Hadith of the Prophet (peace and blessings be upon him) in which he recalled the hilf al-fudul in pre-Islamic Jahiliyyah in which all parties joined hands to support the oppressed and defend the weak. The Prophet stated, “If I were invited to a similar alliance or treaty in Islam, I would welcome the idea.”
Also, any activity that violates Islam is not accepted. Thus, wearing clothes that contain the cross is not permissible. As an alternative, one can use clothes that carry the sign of the Red Crescent which is a branch of the Red Cross organization operating in Muslim countries.
Dr. Su`ud ibn `Abdullah Al-Funaisan, professor at the University of Imam Muhammad ibn Sa`ud, issues the following fatwa: “There is nothing wrong in working with the Red Cross. One of the main objectives of this organization is offering treatment to the sick and taking care of captives, regardless of their religion or nationality. Muslims are always encouraged to participate in charitable actions that aim at promoting welfare and offering a better life for people, so long as such activities do not involve any haram (unlawful) actions.”
As for wearing the uniform of the Red Cross, which has the cross on it, we’d like to make it clear that a Muslim is not permitted to wear such clothes that contain any symbols like the cross or the Jewish star. A Muslim should avoid any symbols that violate the pure and clean `aqeedah (creed) of Islam.
Here is the fatwa issued by the late Sheikh Ibn `Uthaymeen, a prominent Saudi Muslim scholar, that reads: “There is no way to deem it permissible to wear clothes that contain the cross. A Muslim is never permitted to wear it because this is considered an act of propagating the religion of other people and the representation of a creed that violates the Qur’an and the bases of Islam.”