Political Islam is Islam's ideology about unbelievers, kafirs.
The kafir’s favorite theory is that Islam has been "high-jacked" by terrorists and that the vast majority of Muslims are "moderates."
Kafirs keep looking to the moderate Muslim to straighten out this Islam "business". Why doesn’t this happen? After all, Christians will protest when A Christian does something terrible.
Kafirs want to divide Muslims into "moderate" Muslims and "bad" Muslims. A "moderate" Muslim is one who does not want to harm someone. A "bad" Muslim is a terrorist.
These names are based upon a lack of understanding of the dual nature of political Islam. The word moderate has one meaning to a Muslim and another to a kafir. Inside of Islam, a moderate is one who is moderate with the doctrine. A moderate Muslim is one who follows the Sunna (ideal pattern) of Mohammed. Since Mohammed had a dual nature, the doctrine of Mecca and the doctrine of Medina, so Islam and Muslims have a dual nature.
In Mecca Mohammed preached a doctrine where violence was limited to Hell. In Medina Mohammed preached a doctrine of war, jihad.
A terrorist is a moderate Medinan Muslim. Moderation means down the middle. It is Mohammed who defines what is moderate. He used terror, and therefore, terrorism is moderation.
1. Allah made me victorious by awe, by His frightening my enemies for a distance of one month’s journey. [...]"
The nice Muslim at work is a moderate Meccan Muslim. But since the doctrine of Mecca is subordinate to the doctrine of Medina, the Meccan Muslim does not speak out against the moderate Medinan Muslim.
So, the answer to the question, why moderate Muslims don’t protest is that there is no need to protest. The Meccan Muslim knows that what the Medinan Muslim is doing is pure Islam. Why would they protest Islam?
The kafirs are the ones who are confused, not the Muslims. A Muslim who would protest against Islamic terror would not really be a Muslim, but an apostate. Being an apostate is a capital crime in Islam. So even if a Muslim felt like criticizing a terrorist, he would be checked by fear.
Now if you would like to see protests from moderate Muslims, then criticize any aspect of Islam. Then you will see protests from moderate Muslims of both stripes who know that Islam or Mohammed may not be criticized or be the butt of humor. [There has never been a Mohammed joke in 1400 years.] Humor or criticism of Islam are evil and moderates of both Meccan and Medinan Islam will protest, threaten and sue.
Please note the ethical basis of shared community responsibility that is behind the question, "Why don’t moderate Muslims protest Islamic violence?" Muslims do not share our ethics. Islamic dualistic ethics presume that the kafirs are to suffer at the hands of Islam. So based on dualistic ethics Muslims have no reason to give a helping hand. Muslims do not help kafirs. As an example, Islamic charity does not go to any kafirs. When Islamic money went into New Orleans Katrina support, it was given to Muslims, none went to kafirs.
So moderate Muslims are doing exactly what they are supposed to do. The Meccan Muslims are quietly supporting the Medinan Muslims, while the ignorant kafirs sit around wondering, "Where are the moderate Muslims?"