What is Güntheritism?

"Güntheritism is the functional analogue of Lutheranism IRL."

That's the short answer. Theologically, though, it's a case study in steampunk social science.
On the surface, Günther looks very much like Martin Luther, because he fills a relatively similar role: triggering the collapse of the medieval Catholic paradigm and being from the Holy Roman Empire while so doing.

Underneath that veneer of recognizability, though, Günther is a very different beast. Theologically he has a good bit more in common with Thomas Müntzer - partly in attitude (as a participant in the Teutonic Wars, he has the right to be somewhat more cynical and radical about politics than Luther did) and mostly in theology. (Although I can't cite very much, what I've read suggests that Müntzer, and most Anabaptists more generally, reflect a radical critique of Catholicism from within the Catholic tradition, rather than something outside it.) IRL, Hans Küng considered Calvinism, rather than Lutheranism, to be the "truest" Protestantism; that same dichotomy is probably going to be made here, with Farrellitism (coming from a centuries-older tradition) being perceived as "more" Protestant* than Güntheritism.

Güntherite distinctives

• The Güntherite Biblical canon. Truth be told, I'm not entirely sure how the canon itself is distinctly Güntherite, rather than Farrellite, in terms of the books it includes and so forth. What I do know is that the two are translated independently, and into two separate language families - meaning that the northern and southern movements have slightly different Bibles from the start, complicating the history of translation and publication ever after.
• Low German. While it's expanded beyond the Low German world, Güntheritism is very much tied to it. Platt (and specifically Pommersch) has become a *Protestant Yiddish in Andalusada; even if you grow up speaking something entirely different, it's so associated that many of them learn it as part of their ethnoreligious heritage.
• The word "Holy." As Luther objected to "Lutheran" over "Evangelical," so too does Günther object to "Güntherite." His word of choice, however, is "Holy." They may no longer be one, catholic, or apostolic, but ever after Günther's heirs will stand by being the Holy Church. They happily snark about how Catholicism isn't, and when they get into feuds they happily accuse each other of being, as the Scots infamously put it, "wrangly call'd haly."
• A deeply Protestant Mariology. Günther himself is somewhat cynical about Mary's perpetual virginity, but he affirms it himself. His followers, however, are more cynical and less positive about it, in no small part because Marian devotion is characteristic of Teutonic Knights they rebelled against. "Jesus Christ and His sisters!" is a very distinctive Güntherite curse.
• A certain degree of exultation. The Baltic Güntherites are a perfect storm; when they pull together, they successfully fight all contenders to a triumphant standstill. Güntheritism develops a triumphal rhetoric that they never really lose, even after they do lose their invincibility (and expand to Scandinavia, which has no such streak itself.)
• All Saints' Day. Against the cult of saints Günther himself strived in vain, but Baltic Güntheritism eventually reached a compromise and stopped the veneration of individual saints. All Saints' Day is extremely important, and a huge day on the Güntherite liturgical calendar.
• A militant political theology. Orthodoxy's political theology revolves around the concept of symphony; Catholicism's, around the Two Swords and papal primacy. Güntheritism's political thought is founded in the experiences of the Güntherite Wars, when they founded states. The history of Güntheritism is one of tangled relationships with worldly powers, and - throughout it all - of the belief that they can make a holy state. Moreso than any other branch of orthodox Christianity, the Holy Churches believe in the power of revolution.

Güntheritism in the world

Güntheritism is, first and foremost, a Baltic phenomenon. Historically, its core territory is Pomerania and Livonia; it then spread west to Brandenburg, Meckelnborg, and Lübeck (and from there to other key Hanseatic cities, like Frankfurt), and north to Sweden and Norway.

• Scandinavia: Scandinavia was the first region that converted to the Güntherite church rather than being annexed by it. Significantly, they didn't adopt Günther's liturgy; much as per IRL, Scandinavian Güntheritism represents its high-church tendency.
• Scotland: In the early modern era, for political reasons related to the union with Norway, Scotland converted to Güntheritism. It didn't go so well. The Ryal Kirk ("wrangly call'd Haly" in popular culture) was troubled and troubling for its entire history. During the Great Realignment, it was disestablished after the breakup of Scotland-Norway, and officially disbanded just prior to the Imperial Union.

Historically more recently, Güntheritism also spread to a number of rather surprising locations after Pomerania's historic good luck finally ran out. Axamalla, for instance, absorbed considerable numbers of Baltic refugees early in its history; their influence (theological, political and military) are a big part of why it's not part of G.P. Mexico any more. Even more recently than that, the Thousand Days saw a fair number of Güntherites fleeing Scandinavia to settle anywhere else.

Güntherites vs. Guntherists

One of the big differences between Günther's and Luther's careers is that the former fails to establish a safe haven within the Holy Roman Empire. Without a safe haven, Günther flees to the Baltic monastic states (all technically outside the bounds of the Empire), which are undergoing a certain amount of religious strife already, and basically uses the Baltic Revolt as a springboard to build a Holy Church. He leaves behind a number of scattered supporters inside the Empire, which ruthlessly reasserts Catholic hegemony.

Faced with pastoral duties of his own (like establishing a church and catechizing the Balts and Estonians), Günther increasingly becomes tied to Low German and Pomerania, leaving his Imperial, High German followers to work out their faith on their own. (In particular, his Imperial base does not share his late mystical theology.) Because they're theologizing in a very different environment, and can share notes with the Farrellites, Günther's western friends are going to diverge from him significantly enough that by the end of his life he's able to say that "I am not a Guntherist."

For the most part, "Güntherite" refers to the theology and churches that were influenced by Johann Georg himself; "Guntherist" (usually without the umlaut), by contrast, refers to those who were inspired by him and developed it independently. As might be imagined, the latter tend to be much lower-church than the former.