There are a few things that make me uncomfortable about the question, but also about the solutions proposed here. Here are a few thoughts - it's not a full solution, but I think these should be included in any solution we choose:
Questions shouldn't be covert accusations or slandering. All questions should be genuine questions, not rants or blatant advertisements for a position.
Being about a notable individual does not make a question automatically notable. This should go without saying but one thing is asking for clarity on something which a bunch of people already believe -- another is asking for gossip about a notable person.
Medical conditions are not special. They are protected by an expectation of privacy, but so are a bunch of other pieces of information. It's not enough to just protect those.
We can't possibly close questions based on answers before we know them. Even in the case of "current news" close reason, we require conditions which are specific to the question (it must be a news question, with a single news source).
We can't protect only some social categories based on their perceived "utility". I strongly disagree with with any "actress no, politician yes" kind of rules.
Our answers should do no damage. This is intrinsic to our methodology. One thing is to answer with gossip, personal opinions and slandering -- these would be damaging, but those answers are already forbidden. Answers should only be based on already publicly known facts.
Questions about medical conditions of specific people are fine as long as they are strictly notable. They are not automatically notable because they are about a famous person. They need to be specifically believed by a bunch of people. They should be neutral in tone about the answer and describe the claim, not take a position with respect to it.
Answers should be based on publicly verifiable information, not on gossip, innuendo or hearsay. Answers should not take the form of "Doctor Smith, expert on condition but not the person's doctor, said that the claim is true/false", however answers of the form "Doctor Young, expert on condition, after examining directly the patient, says the claim is true/false".