(1) the mission to the Gentiles was the result of Israel's refusal of Christianity, (Act 13:46) an afterthought *. The Church in Israel was dying and had to find a home elsewhere.
It would have died out within another generation. (2) Some are "put in place," or "cued in" (Gr. tasso) for eternal life but through their own will they condemn themselves to lose their place in it. (Act 13:46)
This is novel for some of our friends - the ability to lose their salvation.
(3) Those who believe are destined (not predestined) to eternal life. (Act 13:48)
Thank you; this completes the question's answer. Do you have any questions, Dutch?
It would have died out within another generation
It did — prior to that. The Church in Jerusalem was closed by 62 AD, +James was reportedly stoned to death, Christians were thrown out of the synagogues, and the Pharisaical rabbis resoundly rejected all Christian books and teachings by 99 AD (Jamnia).
A special prayer was included in the morning blessings, one called Birkat Ha Minim, a prayer beseeching God to destroy the apostates.
However, suggestions to the contrary (i.e. [pre]desitnation determined solely by God); almost all are Pauline in character, or attributed to Paul: Romans 8:29-30, Romans 9:11-22, 2 Timothy 1:9, Ephesians 1:4-5, 2 Thessalonians 2:13, 2 Thessalonians 2:11-12.
There is also Jude 4.