Are we Christians suppose to work to have unity with others? This seems to be a recurrent topic among many believers & the world in general, to pursue or work for unity. Many Christian leaders even propose to sacrifice the Truth of the Scriptures in order to have unity with men that worship different gods, or approve sinful behavior, not understanding they are departing from the faith in Christ. The Lord Jesus Christ created a UNITY that we believers are instructed to keep/guard.
-I, therefore, the prisoner of the Lord, exhort you to walk in a manner worthy of the calling with which you were called. 2 With all humility, meekness, and patience, bearing with one another in love, 3 be eager to keep the unity of the Spirit in the bond of peace. 4 There is one body and one Spirit, even as you were called in one hope of your calling, 5 one Lord, one faith, one baptism, 6 one God and Father of all, who is above all, and through all, and in you all. Eph.4: 1-6. -"For by one Spirit we are all baptized into one body, whether we are Jews or Gentiles, whether we are slaves or free, and we have all been made to drink of one Spirit. " 1 Cor.12:13 - so we, being many, are one body in Christ, and individually members of one another. Romans 12:5
Jesus is the Head & we believers are the BODY, there is only ONE body of Christ & ONE Spirit. If we members of the Body of Christ look outside for unity with unbelievers, we are then leaving the body of Christ to become part of a different body which head is not Jesus. There is no true unity, without the Spirit of God. We can be certain, that if people are not doing everything they can to follow the leading of the Spirit, then there will be an absence of unity. "For all who are led by the Spirit of God are sons of God. Rom.8:14 Notice vs. 3, we are instructed to KEEP the unity of the Spirit, not to create unity or be part of the unity the World is creating. What we believers are instructed to do is to pursue peace with everybody, but without forgetting that we are separated (holy) for God. "Pursue peace with all people, and holiness, without which no one will see the Lord." Heb. 12:14 Believers are instructed not to be unequally bond with unbelievers, 2 Cor.6 even used many times exclusively for marriages, in context is not even mentioning them. Of course it can be applied to marriages, but once married the apostle Paul taught that the believer was not to leave his/her unbelieving spouse, 1 Cor. 7:12-16. For this reason many believe that being bound has to do with joining the unbeliever in their sin or spiritual darkness. We find more understanding on the subject when we read other passages of the Bible, like for example, Romans 12, or Ephesians 5, vs. 11 says "And have no fellowship with the unfruitful works of darkness, but rather expose them".  Not all relationships with unbelievers are forbidden; just those that would compromise our faith. We can eat, help, work with unbelievers without committing sin. Jesus, ate with sinners, but did not participate in sin with them (Mark 2:16; Hebrews 4:15). In the 2 Cor.6:14 the Greek word heterozugeo (G2086) suggests an unequal binding together, & we are presented with 5 questions or points of contrasts, which answers are obviously= 'none'.

1We then, as workers together with Him also plead with you not to receive the grace of God in vain. . . 14 Do not be unequally yoked together (G2086) with unbelievers. For what fellowship has righteousness with lawlessness? And what communion (G2842=partnership) has light with darkness? 15 And what accord has Christ with Belial? Or what part (G3310=participation, portion) has a believer with an unbeliever? 16 And what agreement has the temple of God with idols? For you are the temple of the living God. As God has said:

“I will dwell in them And walk among them. I will be their God, And they shall be My people.”

17 Therefore

“Come out from among them And be separate, says the Lord. Do not touch what is unclean, And I will receive you.” 18 “I will be a Father to you, And you shall be My sons and daughters, Says the Lord Almighty.” 2 Cor.6: 1-18

We believers belong to God, we are His children, we belong to one big family & He called us to be separated from sin & the world. There is a difference in been God's creation & God's children. When we receive the sacrifice of His son Jesus & become separated for Him (are led by the Holy Spirit, Rom.8:14) we become His children. “Yet to all who received (G2983=accept) Him, He gave the power (G1849= right, authority) to become sons of God, to those who believed in His name ” Jn.1:12.
So the unity that we have in Christ is part of the grand design. Thus, one of the peculiar marks of the Christian calling is to preserve the unity of the Spirit in the bond of peace. The Character and Nature of Unity A Definition Unity is not a general spirit of friendliness or camaraderie. Nor is unity some common aim or series of aims. Unity is a Product It is the result of all that Paul has been saying in chapters 1-3. It is the product of the cross and God's work in Christ. There can be no Christian unity unless it is based on the teaching of chapters 1-3. Since Christian unity is a result of God's work in Christ, it is not something that we are to aim at for the sake of unity. Unity is “of the Spirit" Spirit is capitalized. It refers to the unity provided by the Holy Spirit. It is a unity which we can never produce. We are not even asked to do so.  - 'The Unity of The Spirit', Bible.org.
I have read some (ecumenical) Catholic sites  were they mention John 17:11 & 21, & also Psalms 133: 1-3, as prove of the need for unity among people of different religions. One site says: "When we come together in unity, the scriptures tell us that God will command a blessing on us. "
"Behold, how good and how pleasant it is for brothers to dwell together in unity! It is like precious oil upon the head,     that runs down on the beard—even Aaron’s beard—. . . for there the Lord has commanded the blessing, even life forever." Psalms 133: 1-3
These verses are not talking about carnal brothers, but it is talking about spiritual brothers & sisters of the same faith in God. Psalm 133 is mentioning Aaron, the High Priest of the Israelites. A wonderful pictures from the Old Testament of the person and work of our redeemer & High Priest Jesus Christ, Christ’s priesthood is superior. He is the perfect and eternal High Priest whose sacrifice and ministry remain, to this day, & more excellent than Aaron’s for several important reasons. One of them, because He is the Son of God made flesh who paid with His death for our sins. More in Hebrews 5:1-10:25. In the previous post & the story of the Tower of Babel in Genesis 11, we see the people are one, committed & united for a cause, but they didn't receive a blessing, quite the opposite. Why? Because they were united for their own man-made cause, to build for their own pride, still, they were united, but united in the wrong things. Things that didn’t line up with God or His Word. So we can see that these Bible verses used as prove of blessings because of unity, got nothing to do with man-made or interfaith unity. Please see more here.