When you start by claiming, “Within Protestantism there is no universal definition of theology or how to understand the Bible…” that risks distortion of the facts. Good though the question is, it needs to be pointed out at the outset that the definition of theology is not a problem, let alone a question, among Protestants. All Protestants are agreed that theology is the study of God (‘Pilgrim Theology’ Michael Horton, p 13 para 1). All Catholics and even non-theists are agreed that theology is the study of God. I respectfully suggest that the word ‘doctrines’ ought to replace ‘theology’ in your opening statement. That might sound pedantic but there is a crucial difference between theology and doctrine, which I hope you will not take offence at my mentioning.
The linked claim, that Protestants have no universal definition of ‘how to understand the Bible’ requires clarification. All Protestants agree that a massive breakthrough in understanding the Bible came with translation of it from Latin into vernacular languages, such translation being based on the original languages of the Scriptures, and not on Latin translations. That was rapidly followed by Martin Luther coming to grips with how the Scriptures exposed doctrinal errors and bad Catholic practices in his era, and deciding to stand on the authority of scriptural teaching alone. That remains the basis for all Protestant unity on how to understand the Bible – on the basis of its supreme authority due to its divine inspiration.
Now, it’s obvious that Protestant denominations have, over the years, diverged in their understanding of some doctrines contained in the Bible, and in orders of service, forms of baptism etc, and I take your point there. I would just say that none of that prevents Protestants authoritatively declaring some beliefs and/or practices to be heretical, due to their Sola Scriptura stance. I would add that that does not entail ‘personal interpretations’ or one of Jesus’ sheep hearing the Good Shepherd’s voice say something another sheep does not hear. What you raise there is the problem common to all Christians in all and every denomination you care to mention: ulterior motives or incomplete grasp of Scripture causing them to attach more importance to some points than other Christians do. The Bible itself warns Christians not to argue about words, or ‘disputable matters’ that cause divisions, but sinful human nature being what it is, that sadly happens. Protestants are more prone to that than Catholics, but surely only because they attach more worth to the Bible, and more time to studying it, than do Catholics, who largely seem happy to just accept doctrine and practice as set forth in a system of sacerdotalism that is anathema to Protestants. It would appear that Catholic bishops make declarations about heresy based on a papal and priestly power and authority structure (sacerdotalism) which the laity just accept, giving an appearance of more unity than with Protestants, when in reality it’s due to unquestioning acceptance of papal authority, not individual desires to plumb the depths of the truth and authority of the Bible. (I gladly allow for individuals like yourself being the exception to that general point.)
All Protestants are agreed on crucial aspects of doctrine, such as those set forth in the Apostles’ Creed, and with that we are united with Catholics and Orthodox. Those fundamentals of the faith are in no doubt and we, like you, and like the Orthodox, do declare pseudo-Christian groups to be heretical due to their deviations from those essential doctrines. Our basis for declaring such deviations to be heretical are exactly the same as yours – the Bible states clear doctrinal matters which must never be deviated from. As stated in the NT letter of Jude, verse 3, Christians are to "contend earnestly for the faith which was once delivered unto the saints". All necessary doctrinal faith was conveyed through the apostles and in the Scriptures by the time the last book of the Bible had been written, which was before the end of the 1st century. Thereafter, there can be no 'new doctrine'. That is the error of pseudo-Christian groups (which part of Grateful Disciple’s answer proves). And that, precisely, is one reason why Luther took a stand against ‘new’ doctrines and bad practices that had crept into the Catholic church of his era. He went back to scripture and compared what he saw there with what he saw going on around him, and the difference was startling. Of course, there was no disagreement regarding essential doctrines such as the bodily resurrection of Christ, the Triune Being of God etc. It was stuff that had crept in over the centuries, new doctrines, that a return to Sola Scriptura exposed as heretical.
I suggest that what you are dealing with in your question are secondary matters that do not enter into the realms of heresy. Protestants do disagree on many secondary issues of the faith, but they would not call those things heretical because they are not essential to salvation. When it comes to declaring any doctrine ‘heretical’, Protestants confine themselves to the fundamentals of biblical doctrine and faith, and they stick to a Sola Scriptura basis for that.
To conclude, I would quote from Martin Luther as confirmation of Nigel’s point, in his answer, that “in genuine Protestantism, the Head of every man is Christ. There is no hierarchy.” These quotes shows why Protestants look to Christ, and not a collective hierarchy of men, to know what Scripture teaches as to sound doctrine or heresy. Here Luther deals with channels of God’s self-disclosure ordained for man – the Word and the Sacraments. Yet the Word is not to be equated with Scripture nor with the Sacraments, though it operates through them and not apart from them. The ‘Word’ is not the Bible as a written book because:
“The gospel is really not that which is contained in books and composed in letters, but rather an oral preaching and a living word, a voice which resounds throughout the whole world and is publicly proclaimed.”
This Word must be heard. This Word must be pondered: “Not through thought, wisdom, and will does the faith of Christ arise in us, but through an incomprehensible and hidden operation of the Spirit, which is given by faith in Christ only at the hearing of the Word and without any other work of ours.”
More, too, than mere reading is required: “No one is taught through much reading and thinking. There is a much higher school where one learns God’s Word. One must go into the wilderness. Then Christ comes and one becomes able to judge the world.”
Likewise, faith is given to those who avail themselves of those outward rites which, again, God has ordained as organs of revelation, the Sacraments. Speaking of God and how he can be ‘found’ in the material creation, Luther made clear that: “…yet he does not wish me to seek him apart from the Word… He is everywhere, but he does not desire that you should seek everywhere but only where the Word is. There if you seek him you will truly find, namely in the Word. These people do not know and see who say that it doesn’t make sense that Christ should be in bread and wine. Of course Christ is with me in prison and the martyr’s death, else where should I be. He is truly present there with the Word, yet not in the same sense as in the sacrament, because he has attached his body and blood to the Word and in bread and wine is bodily to be received.”
Luther maintained that true Christianity is apprehended by faith channelled through Scripture, preaching, and Sacrament. That is why he avidly promoted the study of Scripture in church and school. In church, the pulpit and the altar must each sustain the other. Right doctrine is only obtained through Scripture alone as disclosed via the Word of God. And Christ is the sole revealer. A Christless approach to Scripture will result in corruptions. Source: ‘Here I Stand’ Roland Bainton, pp224-5 (Lion 1988 reprint, Britain)