It is very hard to argue that the challenge of secularism is being met in just one way in “major Muslim societies” (however one defines that term) today. There are many different societies that are majority Muslim and these societies have different relationships with secularism. For example, places like Uzbekistan are officially secular states, places like Iran are officially theocratic, and places like Indonesia are somewhere in between.
If I had to generalize over all “major Muslim societies,” I would say that most of these societies are meeting the challenge of secularism in rather aggressive ways. That is, they are becoming more militantly Islamic and are typically trying to reduce the power of secular forces. This can be seen in a variety of countries.
For example, Turkey has been an officially secular state since the end of the Ottoman Empire. This, however, has started to change as the Muslim world has become more militant and as the AK party has been in power for longer. Secularism is being eroded in this country as the AK party comes to feel more secure in its power. It should be noted, however, that Turkey’s attack on secularism is not particularly violent. Instead, it uses the levers of state power to erode secularism more gradually.
In contrast to Turkey, there are places like Saudi Arabia that are more aggressive in combatting secularism. In Saudi Arabia, there are religious police who go around enforcing religious law. By doing so, they limit the ability of secularism to get any kind of a foothold in their country. At the most aggressive end of the spectrum are the actions taken by some governments and some non-governmental actors to suppress secularism. An example of this is the rise of anti-blasphemy and anti-apostasy laws in places like Pakistan and Afghanistan. Another example is the fact that numerous people in such countries who are seen as secularists have been murdered.
In all of these ways, it appears that many “major Muslim societies” are meeting the challenge of secularism very aggressively. They are using laws and extralegal violence (in various combinations) to combat any attempts at secularization and to roll back secular policies imposed by previous governments.