Jesus NEVER taught that salvation comes with engaging in charitable work on behalf of needy people, nor did the apostles, nor does the bible.
Young's literal, word-by-word translation reveals what this passage actually says:
37 `Then shall the righteous answer him, saying, Lord, when did we see thee hungering, and we nourished? or thirsting, and we gave to drink? 38 and when did we see thee a stranger, and we received? or naked, and we put around? 39 and when did we see thee infirm, or in prison, and we came unto thee? 40 `And the king answering, shall say to them, Verily I say to you, Inasmuch as ye did [it] to one of these my brethren -- the least -- to me ye did [it].
"Brethren" is in apposition to "the least." It means Jesus is speaking of someone who helps out even the least of Jesus' "brethren," that is, those who believe in Jesus.
Clearly, what Jesus is saying is that even the smallest FAITH IN JESUS is rewarded. If that SIDING WITH JESUS is revealed in nothing more fleeting than helping some insignificant believer, then that minimum demonstration of faith in Him is sufficient for salvation.
It seems to me that acts of christian charity are not necessarily limited to other believers, but are extended to all who are in need. Our church's feed the homeless, which does not rely on federal funding, reaches out to men and women in need of simple comforts (food and drink). Where this differs from the liberals' approach is that we are commanded to be directly involved, not indirectly through some government program which absolves tax payers of the responsibility (and benefit) of such involvement.