The apostle Paul is writing about the same thing that happened in Genesis 3. When Adam and Eve sinned, their perspective changed. They were moved away from God and began to look at the events and circumstances of life from a different point of view than they had before.
We know how this works. If we are standing beside someone and looking at an object, say, a tree, both are looking at it from the same perspective and see essentially the same thing. But if we step 20, 30, or 40 feet to one side, the perspective from which we now observe the tree begins to change. Now we see things that may not have been visible when we were side by side with the other person.
That is how it is with God. When we are one with Him, we look at things exactly as He does. When we are not in unity with Him, it is as though we have stepped away from Him, and we begin to see things from a different perspective.
This is the idea Paul refers to here. From now on, we regard no one according to the flesh. Now that we have been converted, we do not look upon others as Japanese, Chinese, Jewish, Russian—this stereotyping begins to fade into the background in terms of importance. To a converted person, the important thing now is whether the other person is converted or unconverted. All that has changed is our perspective, which has changed because we repented in faith. God gave us His Spirit, and a new point of view has entered our thinking.
Let us consider the phrase, “even though we have known Christ according to the flesh.” Paul recounts from his own experience that there was a time when he looked upon Jesus Christ as the great Satan—the enemy of everything that was Judaic. Then he was converted, and his perspective of Christ became, “He is my Savior! He is the greatest thing that has ever happened to humanity!” Same Paul, different mind—his perspective changed.