Strengthen your faith in God's word

In John 17:17 the Lord is praying for his disciples to be sanctified. However, in verse 21 he is praying for them to have unity. How is it possible to be both set apart (divided) and at the same time be united?

This is a misunderstanding.

In John 17:16, the disciples of Jesus Christ are not part of this corrupted world, and by extension, we true believers in Christ Jesus are not part of this world also, just as our Lord Jesus Christ is not of this world.

16. They are not of the world, even as I am not of the world.

So, in John 17:17, we are sanctified, set apart from this world through the Truth, which is Jesus Christ (John 14:6). We, the Church of Jesus Christ, are sanctified and cleansed through the Word of God, which is Jesus Christ (Eph. 5:26), by “the Spirit and belief of the truth” (2 Th. 2:13).

17. Sanctify them through thy truth: thy word is truth.

In John 17:18, since we are no longer of this world, we are now citizens of God’s world because of our Lord Jesus Christ (Ph. 3:20- conversation meaning citizenship). We are set apart from this world for God’s service. We as true believers in Christ Jesus serve in this world as “ambassadors for Christ” (2 Cor. 5:20). We are to remember that we are to be in the world, but not of the world.

18. As thou hast sent me into the world, even so have I also sent them into the world.

In John 17:19, Jesus Christ sanctifies Himself for our sakes so that we also may be sanctified through Him.

19. And for their sakes I sanctify myself, that they also might be sanctified through the truth.

In John 17:20, Jesus Christ’s prayer assures us that He was praying not only for His eleven disciples, but for everyone who would believe in Him. We must put our trust in Him. For He will save anyone who desires to come to God through Him, our Mediator, because “he ever liveth to make intercession for them” (Heb. 7:25). Thus, Jesus Christ made this prayer for all true believers. Plus, the Father already promised the Son that not one whom He had given the Son would be lost (John 6:37-39).

20. Neither pray I for these alone, but for them also which shall believe on me through their word;

In John 17:21-23, Jesus Christ repeatedly says we must be united with God and with each other, even in verse 11 Jesus Christ says we must be one, just as the Father and Son are one. First, since His prayer was for all true believers, He means for us all to be one with each other (verse 21). Second, just as the Father is in Jesus and He is in the Father, so we are to be one with Them, our Triune God (verse 21). Third, the glory of our Lord Jesus Christ is given to us so that we may be one with Him, just as He and the Father are One in Glory (verse 22). Fourth, because the Father is in the Son, and the Son in us, so we are made perfect in one because of the love the Father and Son have for each other and the love They have for us (verse 23).

21. That they all may be one; as thou, Father, art in me, and I in thee, that they also may be one in us: that the world may believe that thou hast sent me.
22. And the glory which thou gavest me I have given them; that they may be one, even as we are one:
23. I in them, and thou in me, that they may be made perfect in one; and that the world may know that thou hast sent me, and hast loved them, as thou hast loved me.

Therefore, we must be sanctified (set apart from this world) through our Lord Jesus Christ, by the Holy Spirit, and we must be united with each other and, above of all, with our Triune God.

Jesus is speaking of setting apart His disciples from the world for service. Of course they should be united in the common cause of the Great Commission.

Whoever thinks this is a contradiction is really grasping. There is no contradiction at all.