The belief you're interested in is Christian perfectionism. Perfectionism was held by a number of people during the Reformation era, and was especially widespread in the low countries. Advocates included Anabaptist Melchior Hoffman, the Reformed Sebastian Castellio, and the nondenominational Dirck Coornhert (Van Veen, 2004).
However, it's also worth considering the context for Calvinist claims of Anabaptist perfectionism. That name has been used as a derogatory epithet from the Reformation until the present.
John Calvin's own frustrations with the Anabaptists
had to do with the fact that the Anabaptists "out-Calvinisted" the
Reformed community on at least two important points. The first was
church discipline. The Calvinists were very critical of Catholics and
Lutherans for their lack of attention to the role of discipline in the
Christian community. The Anabaptists, however, took discipline even
further than the Calvinists, insisting on very tight patterns of
communal control. The Calvinists, obviously stung by this criticism,
responded by labeling the Anabaptists as "perfectionist."
-Mouw, R. J.
(2000). Reflections on my encounter with the Anabaptist-Mennonite
tradition. Mennonite Quarterly Review, 74(4), 571-577. summarizing Balke, 1981
As Mouw describes, Anabaptists can be understood as the extreme perfectionist end of a spectrum in terms of expectations for regeneration and personal transformation, so Berkhof may well be thinking of that spectrum without having any particular writer in mind.
While in this post I'm accepting that the label of perfectionism can be objectively applied to some writers, Perfectionism is usually a label applied by others while rejected by those to which it is applied (Augsburger, 1981).
Often those Christians and groups of Christians who have honestly and
earnestly sought to live a life of high dedication, obedience, and
holiness have not only been misunderstood but also frivolously
condemned as hypocrites or self-righteous. The attempt to strive
toward perfection ("Be ye therefore perfect even as your heavenly
Father is perfect") has often been erroneously labeled perfectionism.
The Anabaptists and Mennonites have suffered under this charge from
-Harold S. Bender, Perfectionism, in Mennonite Encyclopedia.
To be thorough, you'll also want to look into early Christian debates about post-baptismal forgiveness of sins in early Christianity. Tertullian, was highly regarded among early Anabaptists, and they were surely influenced by his position.
For mainstream early Anabaptist authors perspectives on regeneration and quotes that could easily be interpreted as perfectionist, see especially Augsburger, 1981.
Further reading on early Anabaptist perfectionism
- Augsburger, M. S. (1981). Concern for Holiness
in the Mennonite Tradition. The Asbury Journal, 36(4), 28-44. doi:10.7252/Journal.01.1981W.03
- Balke, W. (1981). Calvin and the
Anabaptist radicals. Grand Rapids, MI.: Eerdmans.
- Hughes, R. T. (1986). Christian Primitivism as Perfectionism: From
Anabaptists to Pentecostals. In S. M. Burgess (Ed.). Reaching Beyond: Chapters in the History
of Perfectionism. Peabody, MA: Hendrickson, p. 213-255.
- Van Veen, M. G.
(2004). "No One Born of God Commits Sin": Coornhert's Perfectionism.
Dutch Review of Church History, 84, 338-357.