The paper is based upon focus groups and semi-structured in-depth interviews conducted with women and men in Mexico, Nigeria, Pakistan, Peru and the United States (USA) in 2006. The stigma of abortion was perceived similarly in both legally liberal and restrictive settings although it was more evident in countries where abortion is highly restricted. Personal accounts of experienced stigma were limited, although participants cited numerous social consequences of having an abortion.
But there's no stigma whatsoever to abortion.
No matter how legal abortion is, it will always be understood that it kills a human being. And that will always bring with it a stigma. It doesn't matter how "liberating" it is.