The Baptist hermeneutic is a little different from the rest of the Reformed family.

The Westminster Confession describes the counsel of God as being "either expressly set down in Scripture, or by good and necessary consequence may be deduced from Scripture (WCF 1.6)," emphasis mine.

The London Baptist Confession describes it as "either expressly set down or necessarily contained in Scripture." In short, Reformed Baptists don't "deduce."

Certainly there is continuity between the Testaments, as they are both about Christ. But the New applies in many more ways than just to one geopolitical nation or race. It applies to citizens of a different Kingdom, gathered from all earthly kingdoms. One is temporal type-and-shadow, the other eternal reality.

The writer of Hebrews quotes the Scripture in describing the New Covenant, "NOT like the covenant which I made with their fathers (Heb 8:9)," but one in which "all will know Me (verse 11)." It is "a better covenant" (Heb 7:22), not the same as the Old one.

As circumcision was applied to 8-day-old male citizens of ancient Israel, so baptism is applied to citizens of the the Church (without the distinctions of gender and race) in which "all will know Me," which is why Baptists only baptize believers who give evidence of citizenship in the eternal Kingdom.

Different views of the Covenants
Different Hermeneutics
Different applications of the Regulative Principle of Worship

But certainly Reformed and in keeping with the ancient Creeds and confessions.

-R