When it comes to abortion, I would say, use whatever arguments that are effective, and we probably should first begin with arguments that are appealing to our audience.
If our listeners do not accept our faith, using religious reasons at first could be counter-productive. We need to find out what kind of argument they find acceptable, and what kind of concerns they hold. Most pro-abortionists I find are not evil people. They truly have genuine concerns; they are just often ignorant and blind-sided. You will need to use a lot of secular wisdom to dialogue with their concerns and draw out the truth.
Secondly, ultimately, arguments at best cannot change others, but can only prove to others that we are convinced what we need is love. I discovered long time ago that most conversions to prolife happens not at debates, but at the many clinics and ministries where the pre-abortion doubtful and the post-abortion broken are lovingly cared for, accompanied and healed.
On the other hand, pray for signs and miracles and act on them. While religious arguments today are being frowned upon, a miraculous healing right in front of them is indisputable. Jesus did promise that signs and wonders will accompany those who believe, not just the saintly few, but all who believe. In recent years, there have been a revival of this faith in the Catholic Church. I myself know of a few ministries who regularly go on the street to evangelize. They would walk up to strangers and ask if they have any pain or illness that they would like them to pray for, and healing miracles would often happen. I myself would take every opportunity to pray with people that I meet who need healing, and I have witnessed many healings.
Signs and wonders were given to us not as magic. They were given to all the baptized to exercise in the name of Jesus because people need them to have faith. Today the world has lost its faith. It is time for us to exercise the biblical injunction from Jesus, that we not only go and make them disciples, but also heal the sick, cleanse the lepers, cast out demons, and raise the dead.