Yes, there are moral choices around abortion. Believing the woman is in the best position to make those moral decisions, not the government, is a moral decision. It is a moral decision some can disagree with.
One things I ask the more extreme anti-abortion opponents is "why don't you also oppose contraception?" You can make moral arguments and religious arguments about that and some do. The official Catholic Church position is that life begins before fertilization, you are going against the will of God to interfere with the chance of pregnancy if that is what he decides.
I also ask "what about those who believe the soul enters the body at the first breath?" Jesus Christ is sure to have believed that as a learned Jewish religious teacher of the time.
I could also ask what about that at the time of America's founding fathers, and for hundred of years before, the dividing line between human or not, was quickening, the first time a woman could feel the baby move. Isn't it a moral and proper choice to keep the government out of these decisions in the gray areas and make the human life and murder legal decision at a clear dividing line? Isn't viability, the ability to survive disconnected from the mother, the best measure of a separate human life?
Obama has a good, reasonable moderate view:
I think that the American people struggle with two principles: There's the principle that a fetus is not just an appendage, it's potential life. I think people recognize that there's a moral element to that. They also believe that women should have some control over their bodies and themselves and there is a privacy element to making those decisions.
I don't think people take the issue lightly. A lot of people have arrived in the view that I've arrived at, which is that there is a moral implication to these issues, but that the women involved are in the best position to make that determination. And I don't think they make it lightly.