While yet a new Christian, I became convinced of the Baptist position after reading the works of Alexander Mack, founder of the "Dunkard" Brethren - a sect which many of my ancestors belonged to, and so I was curious about what they believed.
Mack's defense of credobaptism was simple: that after a diligent search of the Scriptures, not a single member of his study group found evidence of an infant being baptized, nor of anyone being baptized by any means other than immersion - and so a consensus was formed to baptize adult members in water.
I thought that Mack, being something of a zealot, must have been mistaken (even perhaps deliberately so) - and so I set out to search the Scriptures for myself, to discern whether or not his claims were true. And so they were, and so I am.
There can be no doubt that when one argues for believers' baptism from the Scriptures alone, one is indubitably doing so in the Protestant spirit of Sola Scriptura.
Mack thought of himself as something of a primitivist, that he was restoring the church to New Testament practices -- to which we can all say, Amen. However, his teaching that an immersionist remnant has always existed in secret, from the earliest times up to the present day, was met with wide derision.
While there were certainly Baptistic movements existing outside of the church throughout the centuries, and we can look back on them with pride and joy that they had the fortitude to defy the establishment, paying with blood if need be, for the cause of God and truth -- perhaps identifying them as "morning stars" of what was to later come -- but the existence of these movements in history does not at all change the fact that the Baptist faith, being a system of theology, is one received from the further Reformation.
Mack's 'remnant' theory was derided not because it was entirely inconceivable, but because it was entirely unnecessary. There is no shame in our Reformation forefathers having recovered what wicked men usurped from God's people, no need at all to appeal to the notion that Baptist truth can stand only if it has existed in perpetuity; it is sufficient to say that Baptist truth did once exist and, by the grace of God, having been restored to the people, that same truth exists now.
The first generation of Protestants put much stock in the necessity of Apostolic succession. Calvin, for example, took great comfort that his Reformed preachers, having once been ordained Catholic priests, were empowered with Apostolic authority by virtue of once having a Bishop's hands laid upon them - and that when those preachers then ordain others, they pass on the chain of 'legitimate' succession from the Apostles.
Baptists have never been concerned about such superstitions. This is the Reformation doctrine of the priesthood of all believers. It is the historical, linear evolution of Protestantism into Puritanism, of further refining the church by steering it from an entrenched episcopal polity toward congregational and presbyterian governance.
We must remember that Protestantism is not a monolith. The magisterial churches, that is the Reformed and the Lutheran, made way for Puritanism and Pietism, which made way for the Great Awakenings, which made way for frontier revivalism; even now we have, for better or for worse, the 'emerging' church and the Charismatic Movement. The point is, Protestantism and Reformation are not things that have happened -- they are things that are happening.
That these movements, being rooted in and directly descended from the Reformation, have impacted the Baptist faith in the way that they have necessarily leads us to two possible conclusions:
1) That the Baptist faith is the primitive faith come down to us from Apostolic practices in the time of the New Testament, shaped and refined by the Reformation to the point where it fits squarely within the parameters of the definition of a Protestant religion, being divided into Arminian and Calvinist camps, &c.
2) That certain of the later generation of Protestants, though professing a multitude of doctrines, yet all having been influenced by Sola Scriptura and the priesthood of all believers, rediscovered the Apostolic practice of credobaptism.
Yes, Baptists are Protestants.