Subjecting someone to unwanted medical treatment is battery, under common law. Starting with long-protected stuff like that makes it seems like maybe we'll be discussing a fundamental right. But the state has a rational interest in protecting the lives of citizens.
But the court never articulates a fundamental right that merits strict scrutiny. Scalia, unsurprisingly, thinks the court should stay away from anything to do with suicide. Rhenquist (maybe to get a majority) distinguishes between assisting suicide and withdrawal of medical treatment.
Again, asking the question gives the answer:
This is a quasi-1A issue.
Note that the state has an interest in preventing divorce (i.e., adultery laws), because of the costs that procedure places on the system.
Does sexual privacy exist only in secret?
And look, this is a privacy case, even though you pretty much don't have any expectation of privacy when you're in the military.