If Zechariah and Elisabeth were righteous by keeping the law, how can righteousness not come by the law?

Luke does not say that Zechariah and Elisabeth became righteous by keeping the law. He says that they were righteous before God and that they lived faithfully by the law: their obedience showed what they were. Paul uses the same word, amemptos (‘blameless’), of himself. Before he met Christ he was, “touching the righteousness which is in the law, blameless” (Philippians 3:6). Yet he did not rely on it, and wanted to be found in Christ, “not having mine own righteousness, which is of the law, but that which is through the faith of Christ” (3:9). Being blameless in the law’s sense, a faithful life that no one could fault, is one thing. Being accepted by God because of it is another.

The law itself never pretended that its keepers were sinless. The “ordinances” Zechariah and Elisabeth walked in included the sin offerings and the Day of Atonement (Leviticus 4; 16), and Zechariah served as a priest in the temple where they were offered. Walking blamelessly in the law meant obeying God and seeking forgiveness by the means he had given. Zechariah’s own song looks for salvation “by the remission of their sins” (Luke 1:77). So he and Elisabeth were righteous as Abraham and David were, by trusting God, who forgives (Romans 4:1-8). Paul’s point in Galatians is about the ground of acceptance. If anyone could be justified by his own law-keeping, Christ’s death would have been needless. Luke’s words do not claim that, and both writers agree.

Righteous through Christ before his coming

John Gill reads Luke 1:6 to mean that Zechariah and Elisabeth were righteous in God’s sight not through their own law-keeping, which can justify no one, but through Christ’s righteousness. In his view, believers who lived before Christ came were accepted on that ground, just as believers are now.