Were the early Jewish believers under constant pressure from the Judaizing Jews?

Yes. Early Jewish believers who embraced Jesus as Messiah were under constant pressure from Judaizing Jews. Scripture notes the churches had rest throughout Judea, Galilee, and Samaria, yet many Jews still became believers, and despite that pressure they were edified, walking in fear of the Lord and comfort of the Holy Spirit.

Les explains that the early Jewish believers, having embraced Jesus as Messiah, were under constant pressure from the Judaizing Jews. He notes archaeology supports that thousands of Jews became adherents, believing Jesus was the Messiah and the Christ. Even so, the churches in Judea, Galilee, and Samaria had rest because the chief persecutor, Saul, was now a saved believer. They were edified, walking in the fear of the Lord and in the comfort of the Holy Spirit, and were multiplied.

Acts 9:31

Then had the churches rest throughout all Judaea and Galilee and Samaria, and were edified; and walking in the fear of the Lord, and in the comfort of the Holy Ghost, were multiplied.

Why did the Jewish believers throughout Judea have rest?

The Jewish believers throughout Judea had rest because the chief persecutor had become a saved believer. Once he was converted, the assemblies experienced relief from that pressure, were edified, and walked in the fear of the Lord and in the comfort of the Holy Spirit.