Thanks for your question regarding Matthew 25:31-46 and it's relationship to the Christian's duty to do good to all people. As I've been reading and re-reading the passage you mentioned, the emphasis seems to fall, not on the responsibility of believers to do good works to all people, but 1) the judgment of the nations at the end of all time and 2) the astonishment of both the sheep and the goats at Christ's evaluation of their service. Notice, first, that before any pronouncement is made concerning good works, those standing before their throne know where they will be sent for all eternity. Sheep are a picture of the people of God (Ps. 24; 100; John 10; 1 Pet. 5:1-5); goats are not. In other words, their home for all eternity has been determined by their identity (those in Christ and those not), not their works. Second, notice the astonishment by both groups regarding the pronouncement of Christ. The sheep are as equally astonished that they had done something worthy as the goats are by the fact that they had not. In the case of the righteous, it is astonishment borne of service that has been gratefully rendered, and then completely forgotten. In the case of the wicked, the expression of surprise is rooted in self-delusion, which is the product of unbelief. In each case, however, what is key is not ultimately what one has done, but whether one is a sheep or goat.
Regarding the passage's relationship to good works toward all, it seems the passage limits such, at least for the sheep, to Christ's "brethren," a term used in the Scriptures for fellow believers in Christ. Perhaps a better passage that calls believers to good works to all men is the one in Galatians 6:10, "So then, as we have opportunity, let us do good to everyone, and especially those who are of the household of faith." In this passage, though there is a priority of service to those in the church, the call is also to do good to those in the world, regardless of their faith in Christ. Another, of course, is the call to love our neighbor as ourselves (Matt. 22:36-40).
Regarding Hebrews 13:1-3: There is some debate as to whether the "strangers" described there are fellow believers whom one does not know (those travelling through a particular area), or someone regardless of their faith in Christ. In the context, it seems that the first position is more plausible since the exhortation in verse 1 is to "let brotherly love continue." In other words, the writer is emphasizing the communal ministry that believers are to have toward one another.
I hope this helps to clarify things in your mind.
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