Walk according to this rule means "understand and apply this principle."
After Jacob's name was changed to Israel, through the centuries Israel gradually became a code name for the called and chosen of God who had made a covenant with Him. Here in Galatians 6, that code name is transferred openly and clearly to the church, and Paul attaches the prepositional phrase "of God" to show possession to differentiate it from the physical nation also named "Israel." God is creating a new nation—a New Covenant people—whose citizenship is in heaven and whose people owe their loyalty to the Kingdom of God, its laws, and its purposes.
The Israel of God—the remnant, the elect, the vessels of mercy, the children of promise—is a spiritual body, the Body of Jesus Christ (Colossians 1:18). There is neither Jew nor Greek, male nor female. In one sense, there is no nationality, for we are being transformed into a new "nationality"—the Kingdom of God! God is doing a new thing.
John W. Ritenbaugh
The Covenants, Grace, and Law (Part 11)