Europe can shut them out but then Europe raises its own costs both financially and diplomatically That really doesn't mean they wouldn't do it. I mean they've already allowed LOTS of people into their countries whose intent is to destroy them. Never underestimate the power of human stupidity.
BTW, you need to proof-read your posts a little better. :)
They think they are replacing their population with one that will be much more obedient. I expect they all think they are going to "convert" at the appropriate moment and segue right into being sultans and emirs. Things, alas, don'[t work that way. Once set in motion a tipping point will be reached, probably well before the Euro projected tipping/conversion point where the new population will simple take over and kill all the ruler types they can catch. If the Euroelite were to make the transition successfully they would after a time find out that thee is simply not room for more than a tiny fraction of them at the top of a Moslem society and the Byzantine murders and usurpations would become constant. A Moslem society that takes over a technologically superior and more prosperous society converts that society very quickly to Arabia and agriculture contracts to a small percentage of what it was. The population level will begin quickly to follow if there is not the USA to bail them out. A Moslem society cannot support the number of people that just about any other society can support. History shows that everywhere that Islam has conquered. As Europe falls we need to cut off access with the newly Islamized lands and work hard to shore up the Central Europe countries that resisted the invasion. Russia is a bulwark for a time but its own Moslem population is gaining while the Great Russians are barely holding their own right now and probably declining pretty rapidly in the long term.
Short term we could launch a major invasion of Europe and clean out the paynim ourselves but that is not terribly likely.