I attended Southern Baptist and nondenominational evangelical (i.e. stealth Baptist) churches growing up. These churches and the sermons preached at them were, as a general rule, heavy on Scripture and practical rules for living and light on doctrine and theology. I don’t recall any explicit supercessionist thinking. When God’s covenants were discussed, it was in the context of “Old” and “New,” and the impression that was left–unintentionally, I think–was that the “Old” were inferior and perhaps obsolete when compared to the shiny and “New.” Of course, if that impression was given, it was a false impression. By its very nature, a covenant from God is an everlasting and unbreakable commitment. The New Covenant instituted by Christ fulfilled the Old Covenants but did not replace or overturn them. Perhaps it would be more accurate to refer to them as the “Old-er” or “Forerunner” covenants, so as not to imply they are somehow obsolete. God’s promises to His people are for all time.