Those who are anti-succession tend to pooh-pooh those faith groups (Petrobrusians, Lollards, etc) as not Baptistic for various reasons, which damages any claim of succession. What were some of those disqualifying aberrations?
I'm not a successionist for a bunch of reasons. In answering your question specifically, I would point out that many of these groups lacked Baptist practices, Baptist theology, and often orthodox Christian beliefs.
When Carroll made his "Trail of Blood" pamphlet, back in the early 1900s, we didn't have as much data on some of these groups. However, 100 years later, we know more about them and can see significant troubles with many.
For instance, the Montanists are a group that Carroll points to as maintaining faithful Baptist theology. However, they are tongue speaking, new revelationists who believed that they could speak new Scripture into existence because of their connection with the Holy Spirit. They ordained men and women to ministry and believe the baptism of the Holy Spirit was sufficient for them. Not exactly a Baptist group. There are more examples but I'll move on.
Tom Butler said:
Is it your position that there have always been New Testament Churches since the days of the New Testament?
Personally, I think this is the wrong question.
One of biggest issues with Carroll's development of the "Trail of Blood" and some others subsequent work on it, was that it is based on a faulty premise. Mainly, that we need to identify churches or movements that authentically carried the Gospel and the marks of the New Testament church from the Apostolic age to present. Quite simply, this isn't a necessary question.
Our calling to Christ is, first and foremost, the calling to be part of the corporate body of Christ. While we have local bodies in which we assemble, our primary calling to the corporate body. So I'm not sure why we need individual faithful "churches" throughout the ages. Our kinship isn't with a church but with the Apostolic faith.
As a result, I think the "Trail of Blood" begins with the wrong supposition. It is inherently flawed from this point.
Tom Butler said:
Can modern-day Baptists (not all of course) claim spiritual kinship if not lineal kinship with the New Testament-era churches?
We are united with churches and believers through all the age in our celebration of baptism and remembrance of communion. We don't need a church to transmit our faith, we need only be part of the Body of Christ to enjoy that kinship.
Tom Butler said:
What variations in doctrine and practice among Baptist churches would disqualify a congregation from claiming to be a New Testament congregation?
Well you've got your marks of a New Testament church and then your marks of a Baptist church. I've provided my list and will stand by it.