The Shiavo case is all about abortion
The "logic" goes something like this:
If you believe that the soul is the seat of consciousness, and
If you believe that the soul is connected to the body as long as it is physically alive, and
If you believe that the perception of the soul is not tied directly to the physical well being of the body
Then it is reasonable to believe that an individual's soul is present and aware of its condition regardless of the physical state of the brain.
The brain has nothing to do with the essence of who we are. The brain is just another collection of tissues of no more importance to defining us then our spleen or lower intestines. Terri Shiavo is as much Terri Shiavo today, in a vegetative state, as she was before her collapse. Thus cutting off life support is as much murder as it would be to stop the beating heart of a fully conscious individual.
The presence of the soul is dependent on the continued life signs of the body. If this were not so then it could be argued that not all humans with life signs have a soul. But that would validate the argument that a fetus may not have a soul in which case abortion may not be murder.
Thus, in order to maintain the assertion that abortion is murder it is absolutely essential to maintain that all humans with physical signs of life are fully in possession of their soul.
To let Terri Shiavo die is to let abortions continue.
(Please note that I am not advocating for this position. I'm only illustrating the necessity of "saving" Terri Shiavo in the radical anti-abortion mindset.)