Per my post #112 These folks were not Jews. They lived in Macedonia, a colony of Rome. Paul was an Apostle to the gentiles.....not the Jews.
Did you even read the passage you quoted?
"Now a certain woman named Lydia heard us. She was a seller of purple from the city of Thyatira, who worshiped God. The Lord opened her heart to heed the things spoken by Paul." (Acts 16:14)
As I pointed out before, these were gentile proselytes to Judaism, like Cornelius in Acts 10. They were following the Jewish customs, including last day Sabbath observance.
If you read the story carefully, you will see that it follows that pattern of Paul, first to go to the Jews in the synagogue to tell them about Messiah Jesus, then to turn to the gentiles, some of whom, like Lydia, were proselytes to Judaism, but had not fully converted.