Islam has nothing to do with this whatsoever, no more than say a Christian shooter in some cinema in has anything to do with Christianity. Islam as a religion has a ton of issues that make this particular kind of thing very hard to get rid of and it is a sad coincidence that many youths that are easily misled are receptive to all sorts of bs but to generalize across a billion or so people because of what a few assholes did is simply wrong.
The puppeteers are the ones that matter, the 'terrorists' are for the most part tools in the hands of masters at playing them believing they are making the world a better place (and how wrong they are).
I make no distinction between idiots of any plumage, be they muslim, Christians, atheists or something else, organized or acting alone. They're a plague on society and should be dealt with, preferably long before they can become a problem in such a way that becoming a problem never even enters their minds because they're too busy living and appreciating life.
There seems a bit of wishful thinking there. We don't know the details but it seems quite likely Islam does have something to do with this.
So even if Islam is nominally involved and even if the fact that religious people have a fringe element (like all people!) that does not mean Islam is the cause of this. Just like Catholicism is not a religion centered around pederasty and just like atheists don't generally go around shooting people.
So the correlation is strong but a lack of tolerance will fuel the generation of more of these, not less.
I recognize your username and I know you are highly intelligent, but how can you ignore all the daily evidence, crime statistics, the shows of intolerance + hatred + violence that Muslims put out towards the natives, all the logic and reason, and all the correlations about the Muslim population in Europe?
The Muslims that I know are very much upset about all this and fear for their future, if anybody is upset at the acts of terrorism by their nominal brethren it is them because they are confronted on a daily basis with the fall-out from all this. The scary bit is that the backlash against them drives them to become defensive and that's the one thing that should not happen.
There is much more to the story than fitting Muslims into the categories of: "non-terrorist" and "active-terrorist".
The fact still remains that Muslim [and other immigrating] populations in Europe negatively impact every single metric of social-ills (rapes, murders, acid-burning attacks, honor-killings / enormous housing and welfare costs / emergence of no-go zones / overall intolerance towards you / and so on and on).
This is the further split of society that you are talking about. It happens when you bring in incompatible groups into your home, and groups that do not reciprocate your good will, tolerance, and open mindedness.
It makes no difference that terrorists are few when double-digits (20%-90%) of Muslims (depending on region and % of population they make up) think that death should be the penalty for apostasy, that suicide bombings are justified, and so on.
The same holds for fascists. Fascists terrorists are driven by their ideology, which in itself can be evil and wrong. That many adherents to an ideology are not violent is in itself not an indication of lack of evil. Even if there were billions of fascists, this wouldn't prove lack of evil of fascism.
The reason that people out of principle will not condemn Islam in western society is that is seen as 'another culture' and a 'minority' in the West. Both aspects are seen as a source for racism, which is bad. But therefore it seems hard to truly look at Islam as a possible source of evil. And I think it is.