Separation of religion and state is next to impossible. Equal is the separation of religion and culture, or of culture and employment. Separation of state and religion requires a split personality or a compartmentalized life. Not an easy task, if it is really possible. So the US expects that it's citizens that are involved in the government are somehow superhuman. This is not reality. The best they can acheive is an effort to not let religion to dictate the outcomes.
Separation would require the ability to make decisions totally rationally, without any emotional feeling involved. Anyone with a triune brain should be capable of doing this, if they can totally detach from the primal, and emotional/automatic portions of our brains for a period of time. As soon as they develop this ability, they separate the cultural/religious portion from reason part, and realize there is a cognitive dissonance between the two, and would not be electable without the automatic portion of the brain. So to be what we need is to fail at elections. Not possible. Duh.