On what basis do Gentiles now have an opportunity for salvation?
Gentiles now have an opportunity for salvation based on the promises made to Abraham. When Israel was set aside, the whole Gentile world was brought into a place of privilege—not that all are saved, but they now have that opportunity because they rest on Abraham's root.
Les explains that when God said Israel aside, He brought the whole Gentile world into that place of privilege. This does not mean they are all saved, but they are brought into a place of privilege where they now have an opportunity for salvation, based again on the promises made to Abraham. For the last 1900 and some years, Gentiles have been resting and feeding on the fatness of the root of Abraham while Israel has been out in dispersion. Les also notes a coming day when God will once again shut the door on the Gentile world, break them off from that grafted position, and Israel will be brought back in and grafted in again, as Paul says in Romans chapter 11, leaving Gentiles again without a Messiah and outside the covenant promises.