Galatians 3:26-29: "26 for in Christ Jesus you are all sons of God, through faith. 27 For as many of you as were baptized into Christ have put on Christ. 28 There is neither Jew nor Greek, there is neither slave nor free, there is no male and female, for you are all one in Christ Jesus. 29 And if you are Christ's, then you are Abraham's offspring, heirs according to promise."
Colossians 3:11-17: "11 Here there is not Greek and Jew, circumcised and uncircumcised, barbarian, Scythian, slave, free; but Christ is all, and in all.
"12 Put on then, as God's chosen ones, holy and beloved, compassionate hearts, kindness, humility, meekness, and patience, 13 bearing with one another and, if one has a complaint against another, forgiving each other; as the Lord has forgiven you, so you also must forgive. 14 And above all these put on love, which binds everything together in perfect harmony. 15 And let the peace of Christ rule in your hearts, to which indeed you were called in one body. And be thankful. 16 Let the word of Christ dwell in you richly, teaching and admonishing one another in all wisdom, singing psalms and hymns and spiritual songs, with thankfulness in your hearts to God. 17 And whatever you do, in word or deed, do everything in the name of the Lord Jesus, giving thanks to God the Father through him.
John 10:16: "'And I have other sheep that are not of this fold. I must bring them also, and they will listen to my voice. So there will be one flock, one shepherd.'"
John 17:11: "'And I am no longer in the world, but they are in the world, and I am coming to you. Holy Father, keep them in your name, which you have given me, that they may be one, even as we are one.'"
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Only some of the stanzas are public domain:
1 In Christ there is no east or west,In Him no south or north,But one great fellowship of loveThroughout the whole wide earth.
4 Join hands, disciples of the faith,Whate'er your race may be;Who serves my Father as His childIs surely kin to me.
5 In Christ now meet both east and west;In Him meet south and north.All Christian souls are one in HimThroughout the whole wide earth.
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To some degree, all of the cited passages appear throughout the hymn with the exception of the third verse. The first two verses draw a bit more from Galatians 3:26-29 and Colossians 3:11-17 (particularly Galatians 3:27 and Colossians 3:11), but all of the hymn's verses (again, with the exception of the third) and all of the cited passages deal with unity in Christ.
The third verse is a response to this unity ("So, brothers, sisters, praise His name / Who died to set us free"), and it seems to come from Colossians 3:12-17, which also flows out of a recognition of being united. The closest resemblance, however, is between the forgiveness mentioned in verse 13 and the freedom "From sin, division, hate, and shame, / From spite and enmity!"