Albert Barnes Commentary Acts 15:9

"and he made no distinction between us and them, cleansing their hearts by faith." — Acts 15:9 (ASV)

And put no difference, etc. Though they had not been circumcised, and though they did not conform to the law of Moses, thus God showed that the observance of these rites was not necessary for the true conversion of people and for acceptance with Him. He did not give us, who are Jews, any advantage over them, but justified and purified all in the same manner.

Purifying their hearts. Thus He gave the best evidence that He had renewed them and admitted them to favor with Him.

By faith. By believing on the Lord Jesus Christ. This showed that the plan by which God was now about to show favor to people was not by external rites and ceremonies, but by a system that required faith as the only condition of acceptance. It is further implied here that there is no true faith that does not purify the heart.