If we used the same logic of separation of church and state, we would not have laws against killing adults either, since the Bible says "Thou shalt not murder." Nor would we have laws against stealing because the Bible commands us not to steal, making it a religious issue. We forget that our constitution and original laws, including laws against abortion, came out of a context of religious conviction and religiously informed consciences. Of course, they were imperfect, in that they allowed slavery and didn't allow women to vote. So laws need to be changed sometimes. But when they remove protection of a person's right to live, no matter how young and small that person is, it's not merely a religious issue, but a universally moral and civil issue, a matter of conscience.
Separation of church and state, even in its right sense, shouldn't mean no law should be in place if religions believe it, but that just laws should be in place regardless of who does or doesn't believe them, religious or secular. But how do you convey that to a generation cut off from history and an understanding of faith and law and conscience and morality?
Look at the Hippocratic Oath in a society that had no Christian influence. No assisting abortions, no physician assisted suicide. Even then they knew.