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Articles pay walled so didn't read it. That said use of religion as a way to influence foreign actors has been going on since like forever. So I'd be interested what the new phenomenon of 'Islamic Soft Power' is.
I've never heard of this phrase anywhere else. I don't think Islamic culture is exalted anywhere outside of Muslim countries (much of the west finds it despicable), so I doubt they have much soft power to speak of. >

I would argue that islamic influence in general is giant negative on any society. islam is an extremely violent, authoritarian, oppressive, and extremist ideology. Many people, especially in the West, can't seem to comprehend just how far out there islam is, there's nothing in the West to compare it to besides itself. 
Now, the reason why islam is all of these things is because islam operates through fear. If you leave islam, you will be killed. If you criticize islam, you will be killed. If you get caught stealing, you'll have your hand cutoff. If you're a woman and you disobey your husband then you will be beaten. If you don't conform to islamic teachings then Allah will punish you by burning you in hell for eternity. Everything about islam functions through the lens of fear. 
islamic cultures are built around this ideology, and so they're going to be reflective of its values and teachings. Of course, not all islamic cultures are the same, they vary wildly from place to place. However, there's a key trend among all islamic cultures. The more in touch with islam a culture is, the more extreme, violent, and oppressive it is. For example countries like Afghanistan, Pakistan, and Saudi Arabia are more in touch with the actual teachings of the islamic scriptures (quran and sahih hadiths) and therefore, their governments and cultures are reflective of that. 
However, when islam isn't the dominant ideology, but is only a broad secondary ideology, things are different. For example, countries like Turkey, Albania, and Bosnia are all islamic, however, they are less in touch with the islamic scriptures and instead have their socities driven by more modern, more secular ideologies. Because of this they are less extreme, less oppressive, and more free and open. 
The more influence islam has on a society, the more it heads in the direction of countries like Afghanistan, like Saudi Arabia, like Algeria. A good example of this would be Indonesia. For the past decades, Saudi Arabia has been trying to do everything it can to get Indonesia to become less secular and more islamic, and they're succeeding. Indonesia over the decades has slowly but surely gotten less and less free. I mean just recently the islamic parties pressured the government to pass legislation that banned adulatory.
I see islam's influence as a negative because whenever it is put against a competing ideology, it is always the worst one. This is best seen when two very similar neighbors decide to take different routes. For example, Algeria and Tunisia. Sample people, same history, same language... yet very different worlds. Tunisia decided to go down a more liberal, more secular path, while Algeria decided to go down a more islamic path. The results are what you would expect. Algeria became a backwards, authoritarian country akin to Saudi Arabia (minus the oil money), while Tunisia became by far the freest country in the entirety of the Arab world (according to the freedom index). Tunisia even became the first country in the Arab world to elect a woman as PM. There are other examples like this like Algeria and Morocco, Pakistan and Bangladesh, Turkey and Iran, and so on.
The point is that the less influence islam has on a society, the better it does. islamic soft power is something that's negative because of what islam is, a tyrannical ideology. When a society allows a extremist, oppressive ideology that enforces itself through fear and violence take hold, then it's going to suffer and decline. I think countries should actively combat and reduce islamic influence, not embrace it. islam is something that holds societies back. >

I think what you’re getting at here is partly the difference between Islam and Islamism, the latter being a political ideology and movement. 
Being Turkish in Turkey is tied to professing Islam and speaking Turkish. Since the founding of the state Islamic faith was part of how the nation was defined even as the ideology of the state was espousal of laicite (Kemalist secularism is beyond what most people understand as secularism in English). In the case of Algeria, Christians and Jews were largely expelled as part of the process of creating a state. This was partly tied to decolonization and prior French divide and conquer strategies. Berbers in Algeria and Kurds in Turkey also present major Muslim minorities which complicated building a state. It’s the political path afterward that’s defining what you’re talking about. 
Turkey and Indonesia are both large Islamic societies (in fact both among the most populous). The influence of Islam on their society is essential.  Islamism is not necessarily an inevitable outcome of their embrace of that fact, nor does their existence outside of Islamism make them any less Islamic. 
While Turkey under Kemalism embraced secularism while Indonesian Pancasila with monotheism is a form of restricted pluralism. I’d say that roughly spans the religious policies seen around the rest of the world (apart from atheism) where one also seems religious and moralistic movements akin to Islamism. The main difference is that Islamism has in recent decades been ascendant across much of the Muslim world.