Here's the unity of the body of Christ that Jesus prayed for - "I in them":
"that all of them may be one, as You, Father, are in Me, and I am in You. May they also be in Us..." John 17:21
"...so that they may be one as We are one— I in them and You in Me—that they may be perfectly united" John 17:22-23
"I in them". That's how we are unified. That prayer got answered when the Holy Spirit was sent into the world to indwell each person who believes. And so, all believers, individually, spread out to the four corners of the world are unified in Christ and each other by virtue of the indwelling of the one Holy Spirit, not by virtue of a one world church institution.
Meanwhile, practical, outward unity of the brethren in the Spirit is achieved by
being at peace with one another,
not by unity of doctrine.
"...the unity of the Spirit through the bond of peace." Ephesians 4:3
Unity of doctrine can't happen, and won't happen in this life, because we're all at different levels of personal growth:
"...until we all reach unity in the faith and in the knowledge of the Son of God, as we mature to the full measure of the stature of Christ." Ephesians 4:13
The simple fact that there are always those still learning and maturing to the full measure of Christ shows us
that unity of doctrine is not possible in this life. Not that God doesn't want us in unity of doctrine:
"I appeal to you, brothers...that all of you agree together, so that there may be no divisions among you and that you may be united in mind and conviction." 1 Corinthians 1:10
But that happens, individually, over time,
as each of us grow in knowledge and understanding, not by virtue of attending a unifying, one and only approved institution as the Catholics insist. Y
our unity of the true people of God in an institutional entity of priests and doctrine is not Biblical. That's not what the unity of the body of Christ is! Our unity is through the Spirit in the bond of peace as each of us in the disunity of our doctrines are growing up into unity of faith and knowledge.