Ruling on giving to a non-Muslim beggar
Question

Is it permissible to give a person money if he is begging on the street, but he isn’t a muslim?
Praise be to Allah.The fuqahaa differed as to whether it is permissible to give charity to a kaafir. The reason for the difference of opinion is that charity means giving something in the hope of earning reward, so will a person be rewarded for spending on a kaafir? The Hanbalis said and it is the well known view of the Shaafais and was also reported from Muhammad in al-Siyar al-Kabeer that it is permissible to give charity to kaafirs in general. This is because of the general applicability of the aayah (interpretation of the meaning): And they give food, in spite of their love for it (or: for the love of Him) to the poor, the orphan and the captive [al-Insaan 76:8]. Ibn Qudaamah said: At that time, captives could only have been kaafirs. The Prophet (peace and blessings of Allah be upon him) said: In (the kind treatment of) every living being there is a reward. Asma bint Abi Bakr (may Allah be pleased with them both) said: My mother came to visit me and she was a mushrik at the time of the Messenger of Allah (peace and blessings of Allah be upon him). I asked the Messenger of Allah (peace and blessings of Allah be upon him), My mother has come to visit me, and she does not want to become Muslim. Should I uphold the ties of kinship with my mother? He said, Yes, uphold the ties of kinship with your mother. Because upholding the ties of kinship is praiseworthy in all religions, and giving to others is a noble characteristic.
Al-Mawsooah al-Fiqhiyyah, part 26.
If a non-Muslim person is asking, it is either of the following cases:

He has an urgent need, such as food, and if he does not receive food he will die. In this case you should feed him, unless he is openly hostile towards Islam, in which case you should refrain. In cases like this, what is given to him should be charity (sadaqah), not zakaah.
His need is not urgent as in the first case, but something may be given to a person like this for the purpose of opening his heart and calling him to Islam, because this serves the overall purpose of shareeah.

And Allah knows best.