To see the root of the problem, one must read the Quran. While Muhammads early teachings were peaceful and did some good for his people, his latter teachings were about hate and violence against all who rejected his teachings. A Muslim who considers him/herself to be a "true" Muslim, must believe that Muhammads latter teachings of hate and violence supercede his earlier teachings.
Islam has no central figure like the Pope and thus any individual can declare themselves an islamic scholar (Imam, Mullah, Cleric). Teaching of the Quran is left to the individual who leads mosque he preaches from. The entity that funds the building of the mosque (Saudi Arabia as an example), decides who can teach.
The problem is that no matter whether the teaching is Sunni or Shia, the ultimate goal remains the same, to conquer the world, destroy all other religions and convert all, forcing non-believers to submit to being a second class populace, enforcing taxes on them and ultimately killing all non-believers.
Those raised in Islamic nations are fed this nonsense from infancy on in their families, their mosques, their required religious indoctrination schools (madrazzas), their friends and so on.
Thus, when some article or cartoon lampoons or ridicules their belief system, the Imams, Mullahs, Ayatollahs, Clerics, seize the opportunity to foment the preached hate in their followers toward the infidels, all with the ultimate goal of suppressing any criticizm of their religion and furthering the agenda of world domination.
The reason for many Muslims not rising up can probably fall into three categories:
1. Work and providing for their families takes precedence.
2. Some aren't caught up in the furor because they've been living in secular western democracies for generations and are happy with it.
3. The Islamic population may be very small in a nation and as such are concerned with their own safety should the host nation and its population get reason to react to any radical movement on the Muslims' part.
For those non-Muslim nations allowing Islam to grow within its borders, they may want to take a good hard look at "all" Islamic nations and how "non-believers" are treated and realise that if Islam gains a majority within their borders, their non-Muslim populace can be expected to be treated the same as their counterparts in Islamic nations, no matter what a Muslim may say to their face. After all, one must remember that the "doctrine of Taqqiya" (deception, lies) is allowed to protect the religion.