So, let's see. The apostle makes it a custom to go into synagogues -- and as a result the Jews would be riled up (Acts 17:1-2). Then he'd go into the synagogue and marketplace daily in Acts 17:17. Then every Sabbath he reasoned in the synagogue (Acts 18:4). As soon as he arrived in Ephesus, he headed into the synagogue and reasoned with Jews (Acts 18:19). Then Apollos did the same thing (Acts 18:26-28). Then Paul spoke for THREE MONTHS in the synagogue (Acts 19:8) and had DAILY discussions in the lecture hall (Acts 19:9-10).
(I suppose your sage advice applies retro-actively to the apostle Paul & Apollos? Paul was this potential raging, seething Jihadist?)
It's at this point that the debate ends and you move on. That's why Jesus advised his apostles to shake the dust from their feet and move on to the next town when their message was not accepted. Likewise he advised them not to cast their pearls before swine in a similar vein.
Please don't try an compare the lucid, spiritual insights of St. Paul with the embarrassing daily mud slinging of the religion forum. If you can't see the difference, you're part of the problem.