Our problem is with “Extreme Islamic Terrorists” who hate us for our tolerance and freedom.
What you are referring to are the people who actually follow Islam. The ones who are "living great lives with us" are not.
Eventually, when the devout followers get sufficient numbers, they will confront their "back slid" fellow Islamists, and demand they follow Islam or they will be regarded as heretics, with the associated bad consequences.
The Islamic religion is like Locusts. For many years they will quietly eat plants until their numbers reach a threshold, then they will launch into a furious swarm and strip everything bare for as far as they can reach.
Islam has murdered more people than even the Communists. It is easily the most murderous ideology in human history.
As others have pointed out, all the Islamic "moderates" do when the true believers are hanging, stoning, and loping off heads is to stand around wringing their hands and saying "Oh dear!"
Your belief that it is possible to coexist with it over a long period of time is very naive based on it's past history.
One does not even have to wait for the future. Just look across the pond at what is happening in Europe now.
Take a look at the people occupying "Sweden's Most Wanted" list. You won't see very many people named "Svenson" on that list.
For an even better understanding, you can look at one of the reasons why the list looks like that. (Graphic Warning.)
Their religion is incompatible with Western Society. We will either refuse to tolerate their religion, or our society will eventually become Islamic, just as is happening in Europe.
One need only look at American muslims that cheer for terrorists. They are street bum, And they are doctors. They live in NYC and rural texas.
Their book tells them to kill the infidel. If they are muslim, they are an enemy of everyone on earth by their own faith.
All the PL that the media and liberals use to spread dangerous excuses do not alert that simple fact. And I am forever amazed how many people are so willing to simply ignore what they themselves believe and say.
Do we see all the ‘great life’ muslims condemn the open terror types? Nope.
Every Navy Seal needs some non combat soldier in supply depot taking his equipment off a shelf and sending it to him.
Every open jihadist has a non open jihadist supplying, propagandizing for and otehrwise supporting them.