The English General Baptists of the early 17th c (Smyth - Helwys) are an interesting illustration of the difficulty of this question.
Smyth was an Anglican lecturer at Cambridge and became a separatist puritan. His congregation left England for Holland in 1608. In Holland the congregation rejected infant baptism. Smyth baptized himself and then the rest of the congregation.
Fellow English paedobaptists challenged this move and askerd why Smyth had not gone to the Dutch Waterlander Mennonites for baptism. Smyth began a dialogue with the Mennonites. His associate, Helwys, rejected this overture as affirmation of apostolic sucession and argued that they had the biblical authority to reconstitute their congregation without Mennonite or other sanction.
Smyth's faction joined with the Mennonites after exchanging confessions of faith. Helwys returned and founded the first batpist church on English soil. A decade later, after John Murton replaced Helwys as the EGB leader, there was an overture for the English General Baptist congregation to affiliate with the Dutch Mennonites. It was rejected because the English General (anti-Calvinistic) Baptists rejected Mennonite doctrines of the ban, pacifism and rejection of oaths. There were NO issues of soteriology mentioned as barriers.
So, the English General Baptists (from the Smyth, Helwys & Murton tradition) I would say are clearly Protestant in some ways and Anabaptist in others. My dissertation demonstrated that the doctrine of salvation of the Mennonites had an impact on John Smyth and John Murton; but not on Thomas Helwys.
I would say that Baptists draw from both the Protestant and Anabaptist traditions in formation of their core doctrines.
It is BOTH/AND.
PS - The sister congregation to Smyth in England (actually they viewed themselves as one congregation meeting in two locations at the time) also relocated to Holland and later became the Pilgrims. They were staunch Calvinistic-paedobaptists.
(See my
WTJ article on Pilgrim Soteriology)
http://www.cybergeneva.org/historic/johnrobinson.asp