None of the conditions are absolutely necessary. On the other hand, the rarity condition is at least as important as the others. If all people had a third functional hand, nobody would think it was a disease. But now virtually all people have two hands and most of the hypothetical three-handers would opt to surgically remove the superfluous limb, even if the third hand can be useful to perform several jobs.

Or more realistically, almost all people have the appendix, which is of no use, except it can host appendicitis. If only 1% of people had the appendix, I am pretty sure that having appendix would be classified as potentially life-threatening congenital disease.

As for your example, if 99% of people has AIDS since time immemorial, are you sure it would be classified as disease? People would have weaker immunity and die younger than they do today - that's all difference. Now we die at 75, with few long-livers who manage to remain healthy up to 90 and die at 100. In the AIDS-permeated society we would die at 25, and those few without AIDS who would manage it to their 50 or 70 would be viewed as anomalies.