Is it possible to be united to another brother brother or sister in Christ based entirely on and only because of our position in Christ (justification), which came to us only by grace, only through faith and only because of Christ. Not because of anything we have done or because of anything else we don't know or do know yet?
Yes, it is possible. In fact it is the only thing which to base our unity on, and to strive for unity because of. What should unite us is the truth of who God is and what he has done for us in his gospel. To have unity over any other thing, might be possible but it would definitely not be Christian unity, and it would not be for the glory of God. Remember the Apostle Paul when he rebuked Peter for causing disunity in Galatians chapter 2 over food and ethnicity? What did he do? He preached the gospel to him. He reminded Peter how they themselves became right before God.
But when Cephas came to Antioch, I opposed him to his face, because he stood condemned. For before certain men came from James, he was eating with the Gentiles; but when they came he drew back and separated himself, fearing the circumcision party.And the rest of the Jews acted hypocritically along with him, so that even Barnabas was led astray by their hypocrisy. But when I saw that their conduct was not in step with the truth of the gospel, I said to Cephas before them all, “If you, though a Jew, live like a Gentile and not like a Jew, how can you force the Gentiles to live like Jews?” We ourselves are Jews by birth and not Gentile sinners; yet we know that a person is not justified[b] by works of the law but through faith in Jesus Christ, so we also have believed in Christ Jesus, in order to be justified by faith in Christ and not by works of the law, because by works of the law no one will be justified. (Galatians 2:11-16)
But is it possible even with the truth of justification, that though it is in fact that great doctrine that is ultimately which creates brothers and sisters in Christ, and is the only reason for unity. But it is possible, that though there has been a unity created by God, that needs to be accepted by us, to also have a need to correct, rebuke and confront a brother or sister who have erred on other substantial essential doctrines?
Yes, it is. This is exactly what we saw Paul do. Unity does not mean tolerance of false doctrine. Unity just means we are brothers or sisters not based on likes, preferences, or cultural things but rather we are brothers or sisters based on the fact we have true faith in Christ.
How a person responds to true doctrine might in time tells us that they are actually a false brother.
In short, sometimes doctrine is meant to divide. And at other times meant to unite. That was part of the point of all the OT prophets teaching, Jesus teaching, and the Apostles teaching. It is meant to separate the sheep from the wolves and the goats. Those who are Jesus's sheep, will hear God's word and follow, those who are not, will not. We don't try to have unity with goats. Possibly faithful evangelistic effort, because the could be one of Gods sheep, they just haven't believed yet, so we don’t know, but not unity. (John 10:16, 25-27, Matt. 13:10-13) Whatever the case, if the truths of God and his gospel are not faithfully proclaimed - it does not really matter, because it would not be the one true God of the Bible we would be winning people to or growing people in, anyway. We also must remember before we go calling and labeling anyone a heretic, that a person isn't downloaded with everything there is to know as soon as they become a Christian. A person when they first become a Christian, I dare say, cannot usually write a dissertation on the Trinity, let alone explain the doctrine of justification. Not only that, but sometimes we forget or drift, and we need to be re-aligned by the gospel. So sometimes we need to be patient, in much the same way we need other brothers to be patient with us.
To God's true people, the truths of Gods word is all that is needed. In fact it is all that is wanted. To the wolves and the goats, well, everything else will be just fine for them.
And remember everything needs to be covered in love and prayer. The best thing to do with false teaching is confront it. Now there are different ways to confront it. Sometimes harshly, sometimes softly, sometimes in between, sometimes in the context of friendship, other times - no. But one thing is true / false doctrine must be confronted and true doctrine must be taught. How people respond will tell a lot. Yes, there is a lot of false teaching out there that needs to be corrected. A lot of the false teaching out there happens because they truly are wolves whom the enemy has sent into destroy. But alas, much of the false teaching is because people don’t know as well. Nevertheless there is still much work to be done. In short - unity is based on truth, not on tolerance. The more truth we have, the more united we can be practically, but positionally we can never be more united or righteous than the moment we first believed. Salvation by grace alone, through faith alone, in Christ alone covers both bases. I would like to offer you a great message to listen to that though it has a specific twist concerning the so called sexual revolution, it offers some great insight from the Bible on how Jesus and the Apostles dealt with different types of people spreading false doctrine. And therefore how we should as well. Do we confront all false teachers the same way? Take a listen to be encouraged. I heard last year in chapel and I would highly recommend listening: Gracious Speech, Salty Language, and the Sexual Revolution (by Joe Rigney) https://vimeo.com/139252824