We can analyze this question in two ways: as it applies to society and as it applies to the novel. First, let us look into the connection between heresy and knowledge.
Heresy is basically going against the orthodox doctrines established by Christianity, mainly, by the church. Disagreeing with, or acting against an established "sacred" dictum would be considered heresy.
Knowledge leads to heresy because it equips the people with information that can be used to challenge the establishment and question its purpose. As a result, the small faction that benefits from the system will be exposed for it. This is why those who rule the system (particularly back in the 14th century when the novel takes place) would make "heretics" undergo great punishments, sending out a very powerful message to the masses: Anyone who dares question the system will suffer.
Seeing that a "heretic" suffers instills prejudice in society, but it is a prejudice against rational thinking, and against making sense of the things that are given to us as facts. It is safe to conclude that, in some societies (think North Korea, for example), knowledge is dangerous, will get you in trouble, and will have people shun you because they do not want to be labeled as rebels, traitors, or "heretics". Regardless of the fact that knowledge is power, in some societies knowledge can be a very risky thing.
Heresy in The Name of the Rose.
Notice that, when a group of people openly disagree with a maxim it is generally due to research or to discovery: a) they have learned that the doctrine is wrong, or b) they have come to the conclusion that the doctrine is only benefiting a group for personal purposes.
These two discoveries are what lead the central problem in The Name of the Rose. The fraticelli knows that the way the church is conducting business is not only wrong, but shameful. The knowledge of these facts endangers the lush lifestyles of the clergy and, for that reason, that particular knowledge is considered to be "heretic".
But why do some people support [the heretics]?"
"Because it serves their purposes, which concern the faith rarely, and more often the conquest of power."
"Is that why the church of Rome accuses all its adversaries of heresy?"
"That is why, and that is also why it recognizes as orthodoxy any heresy it can bring back under its own control or must accept because the heresy has become too strong.”
In the novel, the word "heresy" is used to control the masses; to instill a fear to those who dare to disagree with the current order of things. Therefore, heresy in The Name of the Rose is a double standard.
This double standard is, in part a product of its time. In the 14th century the world was at the very end of the dark ages and right at the primitive beginnings of the Renaissance. Often, when two eras are at an impasse the result is that people stick more sternly to what they know, their beliefs, and their superstitions. It becomes mainly a survival of the fittest.
The Catholic church was a microcosm of what was going on in society, and many in the clergy were beginning to interpret the Scripture differently. Again, it is all a symptom of the changing times, where it was obvious that a new way of seeing things was just beginning.
Since this new way of seeing things consisted on debunking the clergy and exposing them for who they really were, the term "heresy" began to be used as an excuse to get rid of the monks who believed that the clergy had it all wrong; that their lives as sybarites were in complete dissonance with the life of Jesus, who vowed chastity and poverty.
Therefore, the factions that formed within the church were highly prejudiced against one another and would eventually bring the clergy to implode. The cracks in the system began to widen and deepen with the passing of time, and with the increase of people who dared to get and use their knowledge as power.