This example is isomorphic to the Smoker's lesion, with being non-heterosexual = having the lesion, infection = cancer, taking the vaccine = stopping smoking. The recipe suggested in the original post can be extended here: separate the decision to take the vaccine using EDT while not knowing about own sexual orientation (A), the state of having taken the vaccine (E) and the outcome of not being infected (O). Although P(O|E) < P(O|~E), it is not true that P(O|A) < P(O|~A).