It's possible that you will get a response from a historian of comparative religion or some similar field but you are quite unlikely to find a response from anyone dealing with Islamic studies.

As a field, and pretty much systematically, historians of Islamic studies avoid these kinds of analogies. Even seemingly useful terms like "religious revival" are only used with extraordinary caution because of the loaded definitions that they can carry with them from the historical connotations and usage of Christianity.

This kind of comparison between recent Islamic history and the protestant reformation is incredibly popular with political writers and commentators, and some historians of European/Christian history who would rather write about the topic by way of analogy.

But while it might be a valuable political exercise it's difficult to see how it's a valuable historical one. It's a bit like all the articles coming out about how can we compare America's response to the rise of China today to the British response to the rise of Germany a hundred years ago. Sure there are potentially similar dynamics at work, but as a historical exercise it tells you very little about the actual history of what is going on.

You would be much better served by trying to learn about the current sectarian divides and ideological movements within Islam on their own terms than in terms of the protestant reformation. If you'd like I can recommend some books that could be of value to that end.

edit: just to include one for now, I can add more if people want within the limits of what I've studied, Princeton Readings in Islamist Thought: texts and contexts from al-Banna to Bin Laden by Roxanne Leslie Euben is an excellent overview of major 20th century thinkers of political Islam with primary source extracts of some of their major works/speeches.

Not all that well.

The schism in Islam happened in 58 AH (680 CE) and was caused by a disagreement over who would succeed Mohammed. Most differences in doctrine/beliefs happened after that time. The second great schism in Christianity (after the Roman/Orthodox one) happened in 1517 AD. It was about differences in doctrine.

Conflicts between Christians were more about politics than religion. People happened to be of different denominations more because their already established countries were. Modern conflicts in the Middle East between Muslim nations are fairly similar, but conflicts within Muslim countries are more about ethnicity and religion (which are much to a greater degree related in Islam), because some countries' borders are more the result of arbitrary colonial divisions than "natural growth" (i.e. war).

In one case you have the country first and the religion later, in the other you have religion first and countries later. This is a generalisation, and there have been internal conflicts in Christian countries too, but those were more limited and more extreme (more pogrom-ish).

Another difference is the "third party". Both the Anglican Church and Kharijites fought on both sides. However, the latter are all but extinct. Also, the little schism of the Anglicans was predominantly a matter of politics rather than of faith.

There are similarities too, mostly examples of realpolitik. Catholic France supported the Protestant Republic, while Shia Iran supported Sunni Hamas. The Republic represent the interests of the local Calvin Protestant population, like IS propagates their version of Sunni Islam among the Sunni minority in Iraq. There are more similarities, but many more differences.