To whom does God want us to minister? I have given you two passages that speak to this question. Look at where he uses the pronoun - my. When we say they are not my people, let someone else minister to them, we are missing the charge.
Matthew 25:35-40 (ESV)
35 For I was hungry and you gave me food, I was thirsty and you gave me drink, I was a stranger and you welcomed me,
36 I was naked and you clothed me, I was sick and you visited me, I was in prison and you came to me.’
37 Then the righteous will answer him, saying, ‘Lord, when did we see you hungry and feed you, or thirsty and give you drink?
38 And when did we see you a stranger and welcome you, or naked and clothe you?
39 And when did we see you sick or in prison and visit you?’
40 And the King will answer them, ‘Truly, I say to you, as you did it to one of the least of these my brothers, you did it to me.’
John 21:15-17 (ESV)
15 When they had finished breakfast, Jesus said to Simon Peter, “Simon, son of John, do you love me more than these?” He said to him, “Yes, Lord; you know that I love you.” He said to him, “Feed my lambs.”
16 He said to him a second time, “Simon, son of John, do you love me?” He said to him, “Yes, Lord; you know that I love you.” He said to him, “Tend my sheep.”
17 He said to him the third time, “Simon, son of John, do you love me?” Peter was grieved because he said to him the third time, “Do you love me?” and he said to him, “Lord, you know everything; you know that I love you.” Jesus said to him, “Feed my sheep.
God show us who your sheep are and how to minister to them.