Japan doesn't have an 'Islam problem' - the reason of it is quite simple: Japan doesn't mess around in the hellhole known as the Islamic world, and it doesn't commit national suicide via immigration and 'multiculturalism'. There is no need to 'ban' anything, we haven't and will not even 'ban' the more conspicuous forms of Islams (e.g. the Anjem Choudary variety) - but if Europe wants to preserve its culture, peoples and civilization in general, I can't see it as being feasible without emulating something like Japan.
This would entail doing the following:
1. Getting the hell out of the Islamic world and staying the hell out - if the maggot-minded imbeciles of our political class had stayed out of all those American-Israel wars in the first place, perhaps we wouldn't have been in the predicament we are in today.
2. Dealing the coup de grace to the doomed-from-the-start but now certainly moribund failure of a project called the EU.
3. Taking control of our borders - here is where our military is really needed if we want to serve our own national interests, instead of spreading democracy throughout the rest of the world for the Neo-Trotskyists (Neocons).
4. Ending the government subsidized third world immigrant parasitic behavior via reforming the welfare system, and actually attempting to raise the indigenous European birth-rate to the replacement level.
If we do all these then Europe as we have always known it may survive to the end of the century. If not then get ready to go the way of pre-Islamic Persia, Northern Africa, Central Asia and parts of Southern Asia, Europe.