I don’t really like being in the position of defending Kerry, but ...
I think a lot of people realize that true historic Islam was founded and often followed as a brutal system for enforcing the will of the strong against the week. We have at least two choices:
1) Confront Islam as our fathers confronted the Nazis. Point our the historic and current evils and attempt to destroy Islam as a system of government.
2) Oppose any piece of Islam that carries out violence against us or our allies while attempting a support individuals and groups in Islamic countries that are non violent (and might secretly not truly believe in their religion anyway). This includes giving those groups cover against their domestic forces that are presently moderately opposed to us but are in danger of being pushed into the more hard line camp.
I don’t believe the West is currently politically united enough to follow plan 1. Maybe a lot of people who express opinions on this web site are, but the West as a whole mostly is not.
The only thing that I think could unit the West against Islam is fear. I truly hope plan 2 is effective enough to prevent incidents that could lead to plan 1.
What you propose is what has been done at many times in history, and in many places - manage the teaching and preaching of Islam, to steer it away from organized violence. That is a big reason why there is so often a big government role in appointing religious authorities in Islam.
In Islamic countries, they know they have to monitor imams, or they can have a revolt on their hands, a civil war within their society, or an international incident.
Even in countries that have just a significant muslim minority, monitoring and restrictions on teaching and preaching are widely practiced. For example, majority Christian Ethiopia limits the propagation of the more violent interpretations of Islam, appoints the high-level Islamic authorities to the Majlis, and promotes the moderate Al-Ahbash sect.
The well funded wahabbis and salafis are in the streets there now too however, trying to establish radical mosques and trying to raise a covert army of subversives and terrorists.
A country, and a society must have an immune system capable of surviving the types of attacks that Islam wages, and the West has been in denial of this threat, and has stripped away their historical protections. When the doors were open to Islam, we did not receive just a random draw from the population - many of the most pernicious and dangerous elements fled to the West, to escape the repression of their governments (who knew enough to oppress such violent extremists). The muslim brotherhood is now headquartered in London, and the USA is a large fundraising area for terrorist groups.
Your proposal to protect moderate muslims from the extremists is not even really practiced within our own borders - little distinction is made between those who preach militant hate and those from traditionally moderate schools of thought. Indeed, the militants, well funded from the Gulf Arabs, have come to dominate the great majority of US mosques and madrassas, and systematically recruit within our prisons.
Islam has changed all around the globe since Saudi oil money has replaced the Imams and textbooks across the Islamic world, and financed the organization of militant groups.
The bottom Line is that you have to monitor Islam and control violent strains from spreading (with often severe punishments like asset seizure, imprisonment, censorship and expulsion), or it will aggressively attack and deliberately subvert your society.