How does "conservative Baptists" not include IFB churches?
Do you include Pentecostal groups that believe the LORD Jesus Christ did not command the Jewish Apostles to teach all nations and baptize them with water in the name of the Father, the Son, and the Holy Spirit ?
If their only difference from the rest of what i said is baptizing them in the name of the Lord Jesus as the Son in the Trinity (versus sabellianism, and having to speak in tongues as in UPC) then they could be included.
While i uphold the Trinitarian formula, yet as Acts (and the epistles) are interpretive of the gospels, and in which "name" is singular, and only being baptized "in the name of the Lord Jesus" or "in the name of the Lord" is in Acts, like as souls were healed and demons were cast out by the same name, in whose name believers are to do all things, then a case can be made that this represents the authority of the Trinity, as Christ is God manifest in the flesh.
Rome has the formula, but perverts the gospel.
I thought you would know that more about that than me than me.
The short answer is conservative Baptist is used to describe Baptists which are in conventions that Independent and Fundamentalist regard as more Evangelical than Independent and Fundamental, ie., SBC or CBA.
It is unclear whether you are in fellowship with Pentecostals and Charismatics or not. Church of Christ ? Assemblies of God ? It seems to me quite a doctrinal contradiction with Independent Fundamental Baptists.