Paul, as he quotes from Habakkuk 1:5, is referring primarily to the salvation that God had made available through His beloved Son, Jesus. Many would despise such a message (as some in the audience evidently were), and they would perish as result. Salvation was not through keeping the Old Law! There is one other aspect of Paul's teaching here that many Jews would marvel over in disbelief--the opening up of the kingdom of God to the Gentiles. This is something a Jew could not imagine! They despised the Gentiles and had nothing to do with them socially. Recall how difficult it was for this truth to penetrate the mind of the apostle Peter (cf. Acts 10:10ff), though he did eventually embrace it. Paul is warning his listeners to fully accept God's gospel message, including the fact that it is for "everyone" (13:39)--which includes both Jews and Gentiles! Those who cannot accept this fact will certainly perish, along with the rest of those who are disobedient to Christ and unbelieving.
"So when the Jews went out of the synagogue, the Gentiles begged that these words might be preached to them the next Sabbath. Now when the congregation had broken up, many of the Jews and devout proselytes followed Paul and Barnabas, who, speaking to them, persuaded them to continue in the grace of God" (Acts 13:42,43).
The gospel message was so exciting to the Gentiles in attendance that day that they begged Paul and Barnabas to preach it again the next Saturday, to a larger audience, of course. Unfortunately, that's something exceedingly rare--listeners begging for more preaching! Paul and Barnabas were happy to comply; after all, they were there to teach the truth to as many souls as they could. In the days between these two Sabbaths, there were many Jews and proselytes who followed the evangelists and soaked up more teaching. Paul and Barnabas encouraged them to "continue in the grace of God." Since they are exhorted to continue in God's grace, they must already be in God's grace. This implies that these souls had already obeyed the gospel of Christ at some point during the week. Although we have no record of the details, these believers repented of their sins and were immersed in water to have them washed away. They became Christians and were now exhorted to remain faithful (cf. Matt. 10:22). Every child of God should concentrate on continuing in God's grace (cf. II Pet. 3:18). As a side note, it is interesting that some incorrectly teach that God's grace is irrevocable. If it were irrevocable, why would the apostle Paul need to persuade them to continue in it?
"On the next Sabbath almost the whole city came together to hear the word of God. But when the Jews saw the multitudes, they were filled with envy; and contradicting and blaspheming, they opposed the things spoken by Paul. Then Paul and Barnabas grew bold and said, 'It was necessary that the word of God should be spoken to you first; but since you reject it, and judge yourselves unworthy of everlasting life, behold, we turn to the Gentiles" (Acts 13:44-46).
Although we are uncertain as to the size of the city, the fact that most of the residents gathered together to hear the word of God is incredible. There must have been a lot of excitement the entire week, anticipating this time of preaching. Tragically, not everyone was thrilled to see the crowd gathering. The Jews who did not believe were jealous of the influence and success of Paul and Barnabas; they had never been able to draw such a crowd! Although they could not do so logically, they did their best to argue against the gospel message, contradicting and blaspheming it. The evangelists only put up with so much of this abuse before declaring that they would now focus their efforts on the Gentiles in that city, since the Jews were judging themselves unworthy of eternal life (cf. Matt. 7:6). It was proper for them to reach out to Jews first, since the Messiah came from their nation, they were more knowledgeable about God, and they should have been better prepared to obey Jesus' gospel. Some Jews did believe, but many did not. Those who reject Jesus' gospel today (for whatever reason) also judge themselves unworthy of God's salvation, for there is no hope outside the gospel of Christ (cf. Acts 4:12)!