The Gemara says מפרנסים עניי עכו”ם עם עניי ישראל – “We are obligated to support the gentile poor together with the Jewish poor” (Gittin 61a). That means because of darkei shalom, in order to keep peace, we give some charity to the goyim as well. In order to create a good impression, when you’re giving money to a Jewish poor man, and at the same time a gentile comes by for charity, you should be careful to give him something as well. It doesn’t mean that you have to give him the same. But for the sake of shalom, you give him something.
It says עם עניי ישראל – “With the Jewish poor.” Only when they come together. When this נכרי, this gentile, comes by himself, then you’re not obligated to give him anything. He could just think that you’re a tightwad; but not that you’re impartial to Jews. However, you should always be careful, because if it will create animosity, you should make sure to give him something. You’ll have to use your own judgement.