Praise be to Allah.
It is permissible to give charity to non-Muslims and this action will be rewarded, if they are in need of it, but they should not be given the obligatory charity, i.e. zakaat, unless they are those whose hearts are to be softened (i.e., they are close to embracing Islam). It is a condition for giving charity to non-Muslims that they should not be involvied in fighting the Muslims or driving them from their homes, because charity in such cases would be seen as helping them to wage war against the Muslims.(Fataawa Mutanawwi’ah by Shaykh Ibn ‘Uthaymeen, 521).
Allaah says (interpretation of the meaning): “Allaah does not forbid you to deal justly and kindly with those who fought not against you on account of religion and did not drive you out of your homes. Verily, Allaah loves those who deal with equity. It is only as regards those who fought against you on account of religion, and have driven you out of your homes, and helped to drive you out, that Allaah forbids you to befriend them. And whosoever will befriend them, then such are the zaalimoon (wrong-doers – those who disobey Allaah.)” [al-Mumtahimah 60:8-9].
Muslims should seek first and foremost to give their charity to their Muslim brothers who are in need, and there are plenty of them. And Allaah knows best.