If you could write a law that codifies the actual halachah regarding abortion I would support it. It would have to include an absolute permission for a woman to have an abortion if her physical or mental health were in danger (Judaism was far ahead of the rest of the world in realizing that there is no difference), permission for any reason in the first 40 days of pregnancy, and permission when the fetus has a serious defect that is not compatible with life such as Tay-Sachs disease, some trisomy conditions, and developmental problems such as the fetus’s brain developing outside the skull (my wife actually had a patient with such a fetus and had to refer her to an abortion provider).
I am unaware of any Christian group that supports such a position.