A sound, biblical soteriology can be taught, maintained, and defended without subscribing to the bankrupt theology of Calvinism.
This claim is highly demonstrable. If one is not willfully ignorant, all one has to do is look to the first three centuries. Tom Nettles claims that,
"the loss of Calvinism in issues concerning election, depravity, and effectual calling paralleled the loss of inerrancy and soteriological exclusivity and has led to a truncated evangelism that jettisoned the doctrinal foundation for the examination of an experience of grace. This affected not only soteriology, but ecclesiology."
This claim, however, is not demonstrable. It is fallacious and engages in projection, assumptions, and conclusions drawn from assumptions.
Evangelism does not include recognition and warning about the deceitfulness and hardness of the human heart, nor affirmations that only by divine prerogative and power will anyone believe, as that was not in the preaching of either Jesus or Paul, nor the first three centuries of the early Christians. These ideas were prominent among the Gnostics (to which the early Christians rejected as heresy), were then revived by Augustine (the father of both the Roman Catholics and the Protestant Reformation), and then embraced by John Calvin (whose conduct and character did not reflect that of a biblical Christian in the least). These ideas are entirely irrelevant and can be trashed without harm to evangelism, both in message and method.
A soteriology with Calvinism is a path to bad religion and compromised churches. In the past 500 years, the Calvinist experiment has been at work and has failed. Scholars have noted that Calvinism (a.k.a. "TULIP" or "The Doctrines of Grace") has risen up in popularity four times over the past 500 years. Every single time, it always dies back down. Why do you suppose that is? Well, either God ordained it to be such, or else the system just does not hold any water theologically and/or logically. The "move beyond Calvinism" is a move toward biblical religion; the move toward Calvinism is a move toward bad religion, that which mars the eternal nature of God in both His love and His holiness.
The ten-point Traditionalist statement as put forth by Leighton Flowers does have some unbiblical statements within it because it is still holding to certain Calvinistic teachings. However, all one has to do is read the first three centuries of the early Christians to see what the historical teaching of the Congregation has been. If one discerningly reads and carefully pays attention to what one is reading, it is clear that the Bible teaches the exact same things. Leighton Flowers thinks his ten points are entirely biblical, but he could not be further from the truth. He is less wrong than the Calvinist, but he is still wrong. He would do well to study the early Christians. In fact, all professing Christians would do well to study the early Christians. If you want to discover the truth, go to the primary sources; go to the beginning to see what they taught and believed.
Calvinists like Tom Nettles have a problem with humility. Their pride and ego get in the way. They assume that because they have been taught a particular way, that what they have been taught is inerrant and infallible. Guess what? Every denomination believes their systematic to be without flaw. Most Christians lack the humility to consider the possibility that they may be wrong and to subject their entire belief system to extreme doubt and scrutiny. If the Calvinist bothered to pay attention to the random isolated verses they frequently rip out of context by use of proof text methodology, eisegesis, and Scripture twisting, they would discover that their doctrines are abhorrent to actual biblical theology.
Leighton Flowers considers himself a Traditionalist, but several thoughts in his ten points deviate from the traditional teachings of the early Christians from the first three centuries. He would be more accurate if he referred to himself as a partial-Traditionalist.