[o]ur Constitution guarantees separation of church and state. Islam combines church and state. They're using the church part of our First Amendment to infuse their morals in that community, and the people of that community do not like it. They disagree with it.Cain's interpretation of the First Amendment is undeniably erroneous. The separation of church and state is meant to both protect religious institutions from undue influence from the government and protect individuals from undue influence from a state religion. It was never meant to be used as a weapon by communities to persecute or restrict those of another faith.
Even if one assumes that Cain's understanding of Islam is correct - namely that as a religion it is unable to separate its religious doctrines from its conceptualization of the rule of law - his remedy is far from appropriate. Religions or other groups that profess ideologies that run counter to precepts in the constitution are not to be repressed due to their beliefs. Every Muslim may want to turn the United States into an Islamic state (most assuredly do not), yet that would not warrant preventing them from practicing or even preaching their ideas.
Instead, it is the responsibility of the state to disallow violations of the constitution. The courts, for instance, should strike down laws and regulations that violate the precept of separation of church and state, whether such laws are based in sharia, Christian or Jewish law. If such checks function properly (and they largely do), from the perspective of the First Amendment there should be little reason to interfere with the religious practices of any group in America.
Protection of minority religions is precisely why the concept of separation of church and state is necessary. Muslim-Americans should be protected by it not persecuted under it. Whatever their beliefs may be, as long as they stay within the community and are not being forced upon others they should have the right to worship as they see fit. Only when such forms of worship cross the line and lead to religiously-based law should the state step-in to prevent such behavior. A mosque in Tennessee is absolutely acceptable; a law requiring the donning of burqas is not.
Cain's understanding of the constitution and his comments are an embarrassment to all Republicans. Not that this long-shot candidate was every taken seriously, but his perspective is unfortunately damaging to legitimate Republican candidates who have been unfairly linked to this Islamophobic mentality. Republicans need to disavow such candidates and rhetoric if they hope to be taken seriously amongst the pivotal independent voters.