Does Islamic revivalism challenge a stable world order?
Almost by definition, whenever one country or group of countries tries to gain more power, that country or countries challenges the current, stable world order. In the early 20th century, Germany tried to gain more power and it disrupted the stable world order. Today, China is trying to get more power and is, at least to some degree, disrupting world order, particularly as it becomes more aggressive in the South China Sea. Islamic revivalism is no different which is why it does challenge a stable world order to at least some degree.
We can define Islamic revivalism as an attempt on the part of many Muslims to revive their religion and their society. They are trying to make their societies adhere more closely to the dictates of their religion. They are trying to increase the ties between Muslims in different countries, feeling that all Muslims should stand together against other cultures and societies. In a sense, this is a movement for what could be called Muslim nationalism.
This would not necessarily challenge the stable world order, but as things have happened, it does. In this case, one part of Islamic revivalism has been the feeling that Muslims must resist the West and its domination of the world order. When one group of countries feels that another group of countries has too much power, it will try to increase its own power relative to that group. This means that they are trying to change the balance of power in the world. Whenever anyone tries to change the balance of power in the world, it disrupts the world order.
In addition, one part of the Islamic revival has been an increase in religious fundamentalism that has led to an increase in terrorism. There are those who argue that the terrorism is fundamentally un-Islamic, but the terrorists do not agree. To them, they are part of the revival and they are inspired by the same ideas of purifying their religion and society that motivate the revival. Thus, we have to also say that the spread of terrorism and of groups like ISIS is due to the Islamic revival, even if most of the Islamic world rejects the terrorists and their methods. This, too, challenges the stability of the world order.
Just because the Islamic revival challenges a stable world order does not mean that it is necessarily a bad thing. For example, the Civil Rights Movement challenged the stable order in the US, but that order was a bad order. There is nothing wrong with Muslims wanting to revive their religion and adhere to it more closely. However, some aspects of that revival are bad. Moreover, any time that one group of countries tries to increase its power and influence in the world it will challenge the current world order.