Giving to believers or unbelievers?

Orphans, widows, and the poor are well known groups that Christians are commanded to take care of and give to. But what about whether a person is a believer or not? In practice Western Christians try to give equally to both categories - some might indirectly give more to unbelievers.

Jesus' command of love is very well quoted,

³⁴I give you a new commandment, that you love one another. Just as I have loved you, you also should love one another. ³⁵By this everyone will know that you are my disciples, if you have love for one another."  -John 13:34-35

But can we ask why Jesus (speaking exclusively to his disciples at the Last Supper) didn't command them, "By this everyone will know that you are my disciples, if you have unconditional love for all men"? I know this question will likely offend some people but it is a fair question to ask. Jesus was very intentional about what he said and the Apostles were faithful to record him correctly.

Lets look at how the Apostles talked about giving to people. I won't be able to list all the cases and that won't be my objective, it is only to point out a trend in the primary context that they teach giving in. Who is the intended hearer? And who are they supposed to give to?

¹ Now concerning the collection for the saints: you should follow the directions I gave to the churches of Galatia. ²On the first day of every week, each of you is to put aside and save whatever extra you earn, so that collections need not be taken when I come. ³And when I arrive, I will send any whom you approve with letters to take your gift to Jerusalem. ⁴If it seems advisable that I should go also, they will accompany me. -1 Corinthians 16:1

The intended hearer is the Church in Corinth, and they are asked to give to "the saints" in Jerusalem. Read Romans 15:25-26 fore additional information about this giving to poor believers in Jerusalem.

³ Honor widows who are really widows. ... ⁹ Let a widow be put on the list if she is not less than sixty years old and has been married only once;^{c 10}she must be well attested for her good works, as one who has brought up children, shown hospitality, washed the saints' feet, helped the afflicted, and devoted herself to doing good in every way. ... ¹⁶If any believing woman^d has relatives who are really widows, let her assist them; let the church not be burdened, so that it can assist those who are real widows.  -1 Timothy 5-16

The intended hearer is Timothy, a leader in the church at Ephesus, and the church is asked to give to true widows who are in the church.

¹⁴ What good is it, my brothers and sisters,^e if you say you have faith but do not have works? Can faith save you? ¹⁵If a brother or sister is naked and lacks daily food, ¹⁶and one of you says to them, "Go in peace; keep warm and eat your fill," and yet you do not supply their bodily needs, what is the good of that?  -James 2:14-16

The intended reader are believers scattered in "the Dispersion" away from Jerusalem, and these believers are asked to give to "brothers and sisters" in need: other believers.

Obviously, I don't expect anyone to make conclusions about such a big topic from just a few passages pulled from some New Testament books, but none the less I think with more study you will come to the same observations that I have come to: the apostles encouraged believers to give to other believers in need. I don't see the same kind of encouragement to give to unbelievers.

How do we interpret this? And how do we apply this to our giving philosophy?

Can anyone think of some good counter examples? (post comment below)