I would hesitate to be drawn on which medical conditions are acceptable and which should be avoided.
I realize that each case is unique and that we should, ideally, consult a doctor in every case. But sometimes we don't, not for a quick jolly around the circuit.
Obviously, as someone who is not a doctor, I'm using my best judgment as to what I can and can't do. For example, obese persons, even if 100% fit, should not interfere with the full range of control travel and should not lead to an out-of-balance situation, otherwise the flight is off. Somebody with a mental illness, suicide attempt history, epilepsy or a history of not listening to commands should not be able to grab the controls. Somebody who might die in flight, or suffer from narcolepsy or something similar should be restrained with a shoulder harness so that he/she cannot fall forward and restrict control movement. Somebody with a significant physical or mental disability, requiring assistance from the outside to get in/out, should not be blocking the only exit (PA-28 comes to mind). Somebody with a lung disease should not be in a high-flying unpressurized aircraft and you also need to take care when flying at altitude, with somebody who pees or poos in a bag. And so on and so forth.
But are there any medical conditions which might have an unexpected effect on flight safety, which someone who is not a doctor might not think about? Not looking for a full and exhaustive list, but simply stuff I haven't thought of.