By the church's statements, they regarded themselves as Primitive Baptists, which derived from the Separatist movement in England, which was Calvinist, like the Puritans were, but practiced baptism by immersion and operated under a congregational government. (Source: The Baptist River: Essays on Many Tributaries of a Diverse Tradition by William Glenn Jonas)
Unfortunately, for the independent fundamental Baptists' cause, there was no historical continuity from the 4th to the 16th Centuries of continuous Baptistic congregations, as they allege.
I think you may be mistaken, but going with your POV, which I find mistaken, if specific Mosaic prohibitions of illicit relationships are not specifically repeated in the NT (and I don't believe they are), then Independent Fundamental Baptists won't use them for doctrine ? I read his statement of the first distinctive as using "church" as an adjective for all three nouns "polity," "practice," and "doctrine" so that only the NT is used specifically for local church administration. If IFBs have thrown out the OT, they are heretical.