Fred Phelps was not an independent fundamental Baptist; he was five point Calvinist, amillenial, and covenental in theology. Independent fundamental Baptists hold the middle ground between Calvinism and Arminianism, and are premillenial and dispensational. Independent fundamental Baptists are patriotic and recognize the civil authorities are placed in power by God. Conservative Calvinists hold the same views, but Phelps regarded America as cursed from its beginning and his actions, during the runup to the Iraq War and thereafter, bordered on treason. He was as much an outlier among Calvinistic Baptists as Peter Ruckman is among independent fundamental Baptists.Westboro Baptist church was started by Fred Phelps under the sponsorship of East Side Baptist Church (Topeka, KS) after Phelps left Bob Jones University early and started working in the ministry. East Side seems to be an Independent Fundamental Bible Baptist Church. Hmm ...
Today there are at least a hundred different groups which call themselves "Baptist." Many of these churches have conflicting beliefs and practices. The natural question then to ask is, "What makes a person a true Baptist?" In examining the history of Baptists and determining what makes a genuine Baptist, five distinctives should be noted. These five distinctive beliefs separate the true Baptists from other groups who have mistakenly taken the name Baptist, and from all Protestants. Examine any church in light of these five distinctive it will be shown if they are a true historic Baptist congregation.
I did not find the Calvinism and Arminianism test in his explanation of what constitutes an Independent Fundamental Baptist church. He did mention TULIP was "a false view of the doctrines of election, God's grace, and of salvation. I can understand why you want to reassign Westboro Baptist Church to Alex's division but I don't think that works. I'm glad he agrees Calvinism is heresy.
With regard to Phelps' church, it would have failed the first distinctive listed in the source you cited: acceptance of the New Testament only as the authority on matters of church polity, practice, and doctrine. Their condemnations of homosexuals and governments are based on the Old Testament, specifically Deuteronomy and Leviticus.
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.