In the case of mohamed cartoons   many muslims beleive that their "rights" are taken from them....?:
In a free society, there is no such thing as the "right" to not be subjected to offensive things. 

If you read the newspaper, browse the web, watch TV, etc. you will be offended in the West. 

You do have the right to protest (peacefully), picket, rally other people to do the same.

If their "deen" (a Muslim word for faith) is strong, they shouldn't worry about what some non-Muslim has to say about their religion.

Yes, I've seen the cartoons. They're a lot less offensive than what the OFFICIAL newspapers of some nations such as Saudi Arabia, Syria, Iran, etc. say about Judaism