4:28 Paul drew three applications from his interpretation. First, Christians are similar to Isaac in that they experience a supernatural birth and are part of the fulfillment of God's promise. Therefore they should not live as enslaved sons.
4:29 Second, so-called brethren whose origin is different from our own persecute believers, as Ishmael persecuted Isaac. Legalists persecute those living in liberty.
4:30 Third, Christians should exclude legalists from their midst since legalists have no inheritance with the legitimate sons of God. As Abraham cast Ishmael out of his household, so the Galatians should cast the Judaizers out of the church. This does not mean church leaders should excommunicate all legalistic Christians. However, it might be wise to exclude promoters of legalism and nomism if they do not change their teaching. Paul's point was that nomists will not inherit as much blessing from God as those who live by the Spirit.
4:31 Paul concluded his allegorical argument by reminding his readers of the very basic and drastic difference between himself and the Galatians, who were children of faith, and the legalists and nomists, who were children of the flesh.
Paul's defense of salvation by faith alone (chapters 3-4) points out in the strongest terms the incompatibility of faith and works as methods of obtaining justification and sanctification. The Judaizers were trying to get the Galatians to submit to the Mosaic institutions to merit something from God. This approach is antithetic to grace, which acknowledges that people cannot merit God's favor and simply trusts in God to deliver what He has promised.
In this passage Paul contrasted faith and works as methods of obtaining God's favor. Elsewhere he stressed the importance of good works and gave many commands, positive and negative, to guide Christian behavior (e.g., Eph. 2:8-10). In those passages works express the Christian's gratitude to God for His grace. They do not make us more acceptable to God or make God love us more than He would if we did not do them.
What Jesus and the apostles taught about our rewards does not contradict Paul's emphasis here. We should commit ourselves to Jesus as lord (Rom. 12:1-3) and exercise discipline in our lives. We should do these things so we can earn a reward and receive the maximum inheritance possible when we stand before the judgment seat of Christ (cf. 1 Cor. 9:27). However we should do so as an expression of our gratitude (cf. Col. 1:10). We do not need to do so to earn God's favor or love (Rom. 8:31-39).
James' emphasis in his epistle was on the importance of living by faith after God has accepted us (James 2:14-26). Paul's emphasis in Galatians was on what makes us acceptable to God.