I've read the complaint in the federal court case brought by Terri Schiavo's parents. (Available here.) The defendants are the husband, the state court judge, and the hospice.
The claims against the judge are based on the "due process right to a fair and impartial trial," (on the theory that the judge became an advocate for her death) and on a "deprivation of due process" based on the judge's failure to appoint a guardian ad litem, his failure ever to assess Schiavo in person, and his failure to order various tests. The judge is also charged with violating her free exercise of religion in that forcing her to "engage in conduct proscribed by her Catholic faith specifically targets religion for special disabilities without a compelling reason for so doing."
The claim against the hospice is based on the federal Religious Land Use and Institutionalized Persons Act, which, it is alleged, covers the hospice because of its receipt of federal funding. RLUIPA would require a compelling reason to impose a "substantial burden" her free exercise of religion.
The religion-based claims against the judge and the hospice rely on the theory that the Catholic religion requires the continued feeding of a person in a persistent vegetative state and that, even though the defendants are not preventing Schiavo herself from taking an action required by her religion, that those caring for her are required to act pursuant to the requirements of her religion. That seems to be a difficult argument to make, even though, under state law, those caring for her are only able to withhold feeding because they attribute that desire to her. The federal religion claims assume that she must now want what the doctrine of the Catholic church requires, because, when she was able to think about such things, she was a Catholic.
The claim against the husband? I really don't know.
UPDATE: Kevin Drum links to this post and notes that I seem "pretty skeptical." He's right, I am.