If Baptists are Baptist by doctrine, or as Jim puts it 'doctrine, belief and practice', then why would it matter if someone wanted to call the church they are part of 'protestant' to indicate that some time in the past that church's early members had been under the yoke of catholicism and had come out from it (presumably at great cost to themselves)? It would be in the same vein as folk calling their church 'independent' or 'fundamentalist'. The important thing wouldn't be where they had come from, but what they had become.
It would matter only in our endeavor to trace our history. If, in tracing our history, we come to this supposed church, then the doctrinal history would stop there, because before that they were Protestants. This is the mistake that the OP made that led him to believe that Baptists had, at one time come out of the reformation.
But not knowing the exact circumstances of their divergence from the Protestant movement we can only guess at best as to whether or not they had become a true New Testament Church. As I said in another post any authority, including church authority has a source. The original source for church authority is Jesus Christ. This authority is preserved down through the ages by one church begetting (or authorizing) another of the same faith and order.
Yet the argument on this thread seems to be (and I may have misunderstood it) that one simply can't be a Baptist if one's ancestors or one's particular church's founders were folk who came out of catholicism. If that's true, it means that Baptists are not just Baptist by doctrine, but by lineage also--i.e. you can only be Baptist if your ancestors were Baptist (even if not by name).
Again the issue of authority comes into play here. In the illustration you gave above I would have to say that if they just decided to start teaching Baptist doctrine, without any attempt to seek approval of an existing Baptist church, this would not constitute them as a Baptist church.
I keep saying that authority has a source. I am trying to not get too long winded here but perhaps a short illustration is in order. Let's use a police department for an illustration of authority. A police department derives its authority from a government entity such as a city, state or county.
Now, I decide I want to start a police department. I go buy uniforms, badges, police cars and am determined to uphold the laws of the land. Does this make what I have created a police department? Of course not. Why? Because I lack proper authority.
In another thread, GraceSaved was explaining her dilemma of not being near a Biblically-sound IFB church. The reaction of lots of people on this forum was to say that she should start one with other believers at someone's home, even if it meant that they wouldn't have a Pastor to start with.
Now are you saying that if Gracesaved and the other hypothetical believers had been muslims or a catholics before their salvation, then it would be forever impossible for them to group together as a church, no matter their doctrine, beliefs and practice?
No, I am not saying this at all. The advice given to Gracesaved was solid advice and was also predicated by saying that this group that have banded together should seek out the approval of an existing Baptist church. This is a good example of how mission churches are eventually established as a separate Independent Church.
I hope this helps clarify my stand on this issue without having to write and book to explain it.
I suppose one can claim to get authority for their church where ever one chooses but as for me I will seek it from Jesus Christ alone. If I am so led to start an assembly in my home I need not seek sanction from anyone other than God alone. It is Him I seek to please, not some ecclesiastical organization whatever it's name.