Last year I discovered this fact about Mullis and became very curious about how such an eminent scientist could have believed that about AIDS. But, I'd also realized by then that a lot of the so-called "science" about COVID was nonsense and based on invalid methodologies, that often scientists knew their results were wrong but published them anyway, and the whole system seemed hopelessly corrupted by bad incentives. So I didn't write it off, and went looking for his justifications.
It turned out Mullis had written an introduction to a book called "Inventing the AIDS virus" by a (former?) virologist called Peter Duisberg. This introduction laid out his case quite clearly and the book went into great detail, elaborating a theory about why AIDS and HIV are not in fact linked.
I ended up not developing any strong opinions about the merits of the theory, but I will say that it is a scientific theory and not easily dismissed. To do so would require a lot of detail because the people arguing that HIV isn't the cause of AIDS are scientists and have many scientific arguments.
Here is a brief tl;dr summary of Mullis' argument:
1. In the 1980s when AIDS was newly discovered, he was writing a paper about the use of PCR in the detection of HIV. He wrote "HIV is the cause of AIDS" and decided he should provide a citation for this claim, but he wasn't sure which paper actually established this. To his surprise, when he asked around, nobody else seemed to know which paper he should cite for this either, despite it being a by-then standard belief.
2. As he broadened his enquiries and did more research, he came to realize that nobody knew what paper to cite for this claim because none existed.
3. When he tried to find out why there was no paper proving the link between HIV and AIDS, he concluded the whole thing was built on groupthink and a strong desire by certain researchers for it to be caused by a virus, as the field of virology was at that point in deep distress due to the apparent lack of any serious viruses on the scene after the defeat of polio and the lack of any meaningfully sized link between viruses and cancer.
The Duisberg book then elaborated on exactly what was going wrong in a lot of detail, most of which I've now forgotten. But a few claims really stood out to me and I double checked them after reading the book. My fact checks passed, increasing my confidence in Duisberg's claims:
1. That the gender ratio of AIDS victims is radically different between Africa and the west. In the west, AIDS victims are predominantly men and always have been. In Africa there is no gender skew. This makes no biological sense because HIV is a very small virus and cannot know the gender of its host, let alone know/care whether the host is in Africa or not, at least not according to any current theory of genetics or biology. Duisberg provides a much simpler explanation: once AIDS hysteria reached a high enough point, western aid agencies started handing out money in proportion to reported AIDS incidence in a region, and handing it directly to doctors. Combined with the vague nature of AIDS symptoms (it's a syndrome, so the symptoms are the symptoms of whatever disease your broken immune system can't fight off), this gave a strong incentive for doctors to mis-label cases as AIDS in order to get more cash for their clinics.
I verified this claim against a database held by ourworldindata, if I recall correctly. Although the book is old, the claim is still correct.
2. That at some point people started cropping up who had AIDS but were not HIV+. This posed a major problem to the theory, but it was fixed by inventing a new disease with an incredibly long and technical name that had identical symptoms to AIDS but differed only in not testing HIV+. In other words, at some point having a positive HIV test became a "symptom" of the disease, and cases where it was missing were retroactively redefined as "not AIDS", thus making the theory unfalsifiable.
I verified this claim was true by looking up the Wikipedia page and a scientific paper talking about the "AIDS without HIV" disease and confirming the description. Unfortunately I can't remember now off-hand what it was called. I'd have to dig through the book. I recall Duisberg asserting that the name appeared to have been chosen to be very difficult to remember, and I'm inclined to agree.
Note: the same thing has happened with COVID, in which having COVID requires you to have a positive COVID test rather than any specific symptoms.
3. That (western) AIDS never broke out into the heterosexual population in the way that was predicted. That should have happened if AIDS was in fact caused by a virus and AIDS researchers therefore routinely predicted that it would happen ... but it never did. That makes no sense for a disease caused by a virus.
After reading the book I went looking for debunkings of it. The only ones I could find were very poor and mostly concerned with whether Duisberg should be allowed to speak at all. Of the remainder they made arguments that Duisberg had already successfully tackled in his book, so I wondered if there might have been multiple editions. At any rate, it's clear that "mainstream" AIDS science had chosen to simply ignore the problems flagged by Mullis and Duisberg. Given the behavior of health researchers with COVID science I can easily believe the same problems existed back then too.