They are economically important. That's it.
When it comes to other issues like Climate Change, International Disputes, Terrorism etc. and other such issues, not many care about them on the world stage because they have no real say in these matters.
That's a surprise. Muslims countries don't have a say in international disputes? Or issues related to terrorism? Hmm. I wonder where you got that from. Do you remember which countries the US asked for basing rights from when they were trying to attack Iraq? What about when they were trying to attack Afghanistan?
What faith is predominant in the central asian states, which are one of the largest relatively untapped reservoirs of natural gas energy in the world?
Can you name the countries that control the world's most important sea routes, such as the Persian Gulf, the Bosporous/Golden Horn, the Suez Canal, the Strait of Malacca, Strait of Gibraltar etc?
Can you name the country with the second largest armed forces in NATO?
Can you name the city with the world's largest sovereign investment fund?
If you had to guess who the next nuclear power would be, which country would you guess?
Name the countries which provide Europe with its fastest growing group of ethnicities. Here's a hint:
My friend, I think you are mistaken in your analysis of the importance of muslim countries.