This for me is where this breaks down and becomes less clear.
If church and state are to be separated, then when you participate in the democratic process, you must acknowledge the laws as they are written. In the event of abortion, it is not legally or technically considered to be murder. That said, if you advocate against it, or try to use the process to stop it, then you are inserting religion into the process by proxy. So how are these ideals reconciled with our beliefs?
The State's primary goal is to uphold the stability of society, which is why they are (and should be) concerned with ethical questions. Abortion is an ethical question, and I believe that their is as much a scientific argument for it to be considered murder as a theological one. Moral questions, like whether sexual immorality ought to be outlawed, is not normally an interest of the State.
Separation of Church and state, however, is most effective to avoid confusion. We have spiritual counselors (Pastors, Priests, etc.) and we have temporal magistrates (Presidents, Governors, Prime Ministers, etc.) but we have only one Spiritual Magistrate, and that is God. No one should be confused whether a spiritual counselor is also a spiritual magistrate, hence the separation.