Islam in general lacks self reflection and is very dogmatic, because it did not go through Reformation like Christiniaty.
By and large, I expect the european countries - aside maybe eastern europe - to go through islamization. It is literally the same pattern as the Roman empire went through with Christianity. Originally deemed small and unimportant sect it was gradually growing by converting people into christians due to being open thus anybody could join, while paganism was in decline and I would not be surprised that by the end even common folks hated it because "it was the religion of elite" or "sexual depravity" and "corruption" - same with roman catholic church now.
With Islam it is slightly different as bunch of views in Islam are not compatible with the western views, but muslims compensate that by having a bigger population and growing. Would not be surprised that eventually some european states might bring the state religion again (let's say in 50 years), as Quran does not separate the state and the church and thus folks will be ok with that. We literally have folks being happy to have "Quran of Nature" or whatever it is. In general, the ruling elite might even welcome Islam due to that - imagine being able to influence the common people (like imams do) just by having the higher position of power, without need to go through the political dance that much. And I would not be surprised that somebody will do that to gain votes. Plus, Islam is pretty compatible with some of modern values - like not eating pork (and with the current fight against factories and meat production it fits quite nicely). In general, I think some folks will welcome Islam simply because it allows to shape all parts of the society.