Law and morality differ in a very simple way. Law comes from a community, morality is personal.
To separate church from state you need to know why you are doing it. First, you live in a country where you are free to disbelieve in as many gods as you like. So if you are free to disbelieve in Allah then you shouldn't have laws telling women they need to cover their heads in accordance to Islamic law. If you are free to disbelieve in YHWH than you should be able to work on Saturday. If you are free to disbelieve in Jesus than you should be allowed to masturbate. Giving the populous the right to not believe in religion and then forcing them to pray in school, post the ten commandments at court rooms, not allow gay couples to marry, not allow a woman to treat her body as if it were her own is disgusting. I doubt you'd allow Scientologists to make a law banning psychology, so how could you sit by and allow Christians to make Christian laws for non-Christians?
I think the major problem is people think religion and morality are related. I have morals, I would try to never let myself, through malice, negligence or ignorance, injure someone else (mentally, emotionally or physically,) and I am anything but religious.