Answered by Sayyidi Habib Umar bin Hafiz (may Allah protect him and benefit us by him)
Is it permissible to give zakat money to non-Muslims?
One of the categories of people who qualify to receive zakat are ‘those whose hearts are to be reconciled’ (al-mu’allafah qulubuhum). This term has two meanings. The first is those who have recently embraced Islam but are still weak in their resolve and in their faith. The second is those who it is hoped will embrace Islam, especially if they are given some zakat. Some scholars follow the second interpretation. So if all the needy Muslims in the community have been given some zakat then it is permissible to follow the second opinion and give to those who are close to Islam. It is better, however, that they be given money which is not zakat.