Is it permissible to give charity and zakah to non-Muslims?

Yes, it is permissible to give charity to non-Muslims in order to soften their hearts towards Islam, with the hope that they will become Muslim, whether it is zakah or voluntary charity. With regard to other purposes, it is permissible to give them voluntary charity but it is not permissible to give them zakah, because Allah says (interpretation of the meaning):

“Allah does not forbid you to deal justly and kindly with those who fought not against you on account of religion nor drove you out of your homes. Verily, Allah loves those who deal with equity” [al-Mumtahanah 60:8]. 

With regard to zakah, it is not permissible for a kaafir unless he is one whose heart is to be softened towards Islam, because Allah mentions among those who are entitled to zakah (interpretation of the meaning) “and to attract the hearts of those who have been inclined (towards Islam)” [al-Tawbah 9:60]. End quote. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him). 

Al-Ijaabaat ‘ala As’ilah al-Jaaliyaat, 1/24, 25