Jesus' prayer in John 17 is that "they all may be one, as Thou Father art in Me, and I in Thee, that they also may be one in us..."
Is there any disagreement between the Father and the Son? Do they ever have to "agree to disagree"?
And this is the "template" of unity which the Son of God prays the Father to bring us into as well. Nothing less.
And so Paul, one of the messengers of the Son of God, beseeches "that ye all speak the same thing, and that there be no divisions among you; but that ye be perfectly joined together in the same mind and in the same judgment" (1 Cor. 1.10).
Paul beseeches for this, not on the basis of our own ability to come to this kind of unity, but "by the name of our Lord Jesus Christ." "I beseech you, brethren, by the name of our Lord Jesus Christ, that ye all speak the same thing..." In other words, there is provision in His Name for this kind of unity.
So we must know that this is what we in the Church are headed for. This is what God has in mind for the Church under the New Covenant, and, impossible as it is, He has what it takes to bring it into being. And is going to do so. He will not settle for less.
Meanwhile, when Paul writes to the Ephesians of the seven-fold facets of unity, he brings up that little word, "forbearance."
"I therefore the prisoner of the Lord beseech you that ye walk worthy of the calling wherewith ye are called,
With all lowliness and meekness, with longsuffering [patience] forbearing one another in love;
Endeavouring to keep the unity of the Spirit in the bond of peace" (Eph. 4.1-3).
We know where we are headed-- being made one even as the Father and the Son are one.
This-- lowliness, meekness, patience, forbearing [bearing with] one another in love-- is God's provision for us along the way.
Edit to add: With this in mind, my answer to the question in the OP is, "Yes, they can, and ought to."