The government can't tell religious orgs what to do (within reason). Religious doctrine cannot be used to craft government policy.
So you're saying that public policy that stems from the religious motivations of individual legislators can never be, but if it's from the religious motivations of athiests, it's OK?
No. That's not what I said, and this doesn't even make any sense. Atheists have no religious motivations because they do not believe in a higher power.
Religious beliefs motivate all sort of legislation and public policy. There is a difference between codifying Religious Doctrine into law and crafting secular public policy based on the motives of the religiously minded.
Explain to me the difference between, for example, explicitly banning gay marriage because of the Bible's stance on homosexuality, and banning gay marriage because the personal moral convictions of the legislators are rooted in those biblical teachings.
If the end result is the same (a ban on gay marriage due to the teachings of one religion), then there is no real difference.
One religion being socially or poltically dominant enough to elect legislative majorities that will use that religion's teachings as the basis for public morality isn't a violation of the separation of church and state.
The historical context that led to the Enlightenment's "separation of church and state" doctrine was established state churches holding special status and conferring special privileges under the law. That these two corporate entities (i.e., the church and the state) are legally distinct is the only requirement; secularism is something entirely different.