This is sort of the opposite version of a question I just asked.
What is the most popular belief system that rejects all points of Calvinism and Arminianism? It seems to me that Calvinism and Arminianism would cover all doctrinal bases.
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Whether or not you'll find a theology that rejects everything in Calvinism and Arminianism is going to depend on how broadly you define those terms (as Calvinism can also encompass such issues as infant baptism, eschatology, and the relation of the OT civil law and modern day governance). But the closest you'll find (at least in matters of salvation) is probably Pelagianism.
In Pelagianism, the necessity of the grace of God in salvation is denied, though Pelagius did say that people were often helped by it. Calvinism, being rooted in Augustinianism, would say that God's grace is not just necessary, but also sufficient for salvation. Arminians would also affirm the necessity of God's grace.