The existence of Islamic doctrine presents the non-Muslims of the world with a problem. On the one hand, being a Muslim — at least in theory — means believing in the written Islamic doctrines (the words written in the Koran, the Hadith, and the Sira), which advocate relentless striving to bring all the world under the rule of Islamic law (and authorizes the use of force to do so), teaches that women are worth less than men, and teaches non-Muslims are "the worst of creatures," among many other equally unsavory teachings.
On the other hand, many people who call themselves Muslims don't abide by most of those teachings. They either don't know about the teachings, or they have decided not to follow them. This group may, in fact, be the majority of Muslims.
But the existence of even a majority of Muslims who ignore the written doctrine doesn't prevent Islam from being a problem to non-Muslims. Enough Muslims believe that the Islamic doctrines are valid and strive mightily — even to the point of death — to put those doctrines into practice. And many of them are actively trying to reach the more ambivalent Muslims of the world and convince them that because they don't follow the teachings, they are hypocrites, which is a very bad thing according to Islamic doctrine. So bad, in fact, the penalty for it is death.
A study in Britain found this surprising fact: The children of Muslim immigrants are more likely than their parents to be "radical" (to believe Islamic doctrines should be followed diligently). Recruiters talk to young teenage Muslim boys and tell them that their parents are hypocrites. They are told to read the Koran for themselves and then look at their parents and ask, "Do they actually follow the teachings, or just give it lip service?" And what teenager isn't happy to deride their parents for being hypocrites? But it pushes them toward fundamentalism.
Another aspect of our problem is the indiscriminate acceptance of Muslim immigrants into free countries, and then a lack of pressure by the host country to integrate them into the larger society, which creates the conditions for what Daniel Pipes called "semi-autonomous sectors" to develop. Others have called them (somewhat — but only somewhat — mistakenly) "no-go zones." These are areas where Muslims concentrate, and as their numbers increase in that area, the more devout among them start exerting pressure on the rest of the Muslims to conform to Islamic standards. And of course, the Muslims-in-name-only cannot successfully argue against these Islamic standards because it's all written down in clear and forceful language in the books they supposedly believe are sacred. So they conform. The women cover up. The men attend the mosque (or they are harassed), dress differently, grow a beard, etc. The non-Muslims in the area are also harassed until they move away, making room for more Muslims to move to the area.
This is all in accordance with Islamic teachings and the example of Muhammad: If a group of Muslims can, they should enforce Islamic standards (they are Allah's standards, after all, and should be the standards for all people), and when Muslims gain political power, they should impinge these standards on everyone, including non-Muslims.
This manifests itself in a different way by shutting down free speech by force. When the Charlie Hebdo cartoonists made fun of Islam, for example, 12 of them were murdered for it. When Theo Van Gogh made a film critical of Islam's treatment of women, he was shot to death. Salman Rushdie wrote a novel critical of Islam and the devout Islamic ruler of Iran ordered his assassination. So far, he has avoided being murdered. The examples go on and on.
Muhammad himself did the same thing. And it says in the Koran (91 times) that a Muslim should follow Muhammad's example in all things. People during Muhammad's lifetime were assassinated with Muhammad's approval or request for the "crime" of criticizing Islam or Muhammad.
To some degree, the method has worked: Islamic standards have been imposed on non-Muslims. The Islamic standard referred to above says nobody can make fun of Islam or Muhammad. By rioting and killing, devoted followers of Islamic doctrine are instituting this Islamic rule worldwide on everyone. After the 2006 "cartoon riots," very few newspapers in the world had the courage to re-publish the cartoons. Almost everyone was cowed into silence. In other words, free speech was shut down on that subject. There was even a book published about the whole event, and the book didn't even show the cartoons! It wasn't quite as bad after the Charlie Hebdo shootings, but many major newspapers refused to re-publish the cartoons.
Another problem with Islam is that the penalty for leaving the religion is death. Freedom of religion is not an option with Islam. The death penalty is actually enforced in some Muslim countries, and a reasonable argument could be made that it is enforced in some non-Muslim countries too, if we count Muslim parents killing their daughters for going out with a non-Muslim boy or in other ways acting non-Muslim. These are called "honor killings" and they are carried out because the parents are following the written Islamic teachings.
In other words, many of the regular, mainstream teachings of Islam are major human rights violations when they are put into practice. We can't ignore this problem, but we can't really "solve" it either. What can be done when a billion and a half people claim allegiance to an ideology that is incompatible with freedom of speech, freedom of religion, and human rights, especially for women? Going to war with all of them would be ridiculous. Not doing anything at all would be equally ridiculous. But what can be done?
That's the problem of Islam.
So far, we have only one strong conclusion: The solution will begin with learning what Islam really teaches and dealing with an accurate understanding of the written doctrine, rather than trying to make each other believe things that aren't true. Whatever solutions non-Muslims come up with should at least be based on reality and not on wishful thinking. That much seems clear. Learn some ideas about what might be done here.