Once again, vaccines don't "induce" mutations. Pathogens are not sentient hive minds searching for weaknesses in our immune system so that they can kill us. Mutations occur naturally and randomly in all organisms. The vast majority of them are harmful to the organism. Much more rarely, they provide some kind of survival/reproductive advantage, which makes the organism more likely to survive and reproduce and thus pass on the advantage to its descendants. The main reason that viruses typically evolve to become less deadly over time is that a virus that kills its host shortens its own window to spread to new hosts, so over time, strains that are less deadly have more opportunities to reproduce than deadlier strains, and the latter gradually get supplanted by the former.
All of this is important because the papers at the heart of that article that you linked to suggest that "leaky"/"imperfect" vaccines that don't provide sterilizing immunity could allow those more deadly strains to continue to reproduce in vaccinated individuals, who could get infected without ever getting sick, so that these strains never get selected out of the gene pool. This
is not relevant to a vaccine that reduces or eliminates transmission, which, as one of the papers notes, "is the case for nearly all vaccines used in humans" (and, as I noted in my previous post, seems to be the case for at least the Pfizer vax and probably the others as well).
You keep talking about HIV, but HIV mutates rapidly and covid does not, and this is why no vaccine currently even exists for HIV. And you are speculating about a hypothetical HIV vaccine "inducing" (as you put it) a mutation that would make HIV easier to acquire, but that isn't what your article talks about. The article is about the potential for non-sterilizing vaccines to block ordinary selective pressure against more deadly strains of a pathogen, and the theoretical relationship between the vaccine and the more deadly strain's reproduction and spread is clear. It's true that, through random mutation, strains could also emerge that are easier to catch and/or less susceptible to the immune response provoked by the existing vaccination (preliminary evidence suggests that the UK variant might be easier to catch and that the South African variant might be less affected by the J&J vaccine, for instance), but there is no proposed relationship here between the new strain and the vaccine in which the vaccine actually facilitates the reproduction and spread of the new strain. And on the contrary, to the extent that the vaccine provides sterilizing immunity and/or otherwise reduces or eliminates transmission, more vaccinated individuals = fewer opportunities for the virus to reproduce = fewer opportunities for spontaneous mutation.
Casting doubt on the vax because your uncle had to sign a liability waiver and the vax is "experimental" is another classic conspiracy theorist tactic, so way to go there. I'm pretty sure I've had to sign a waiver literally every time I've gotten even the annual flu shot. I suspect that my parents probably had to sign waivers when I received my various childhood vaccinations. Liability waivers are, uh, not unusual. And while I don't know exactly what the waiver your uncle had to sign said, the fact sheet that is required to be provided with the Moderna vax is
easily found on the internet (as are the
fact sheets for the other vaxxes), and it just discusses all of the ordinary side effects (rash, feeling ill, etc) and potential complications (e.g., allergic reaction), which are par for the course with any vaccine. None of this has anything to do with your supposedly primary concern about "vaccine-induced mutations," of course, but pointing out that the vax is "experimental" and hasn't received FDA approval is just another way to plant the seeds of uncertainty about the vaccine. You seem to have this idea that, under the ordinary approval process that the FDA has not had time to undertake for the covid vaccines, a new vaccine is specifically studied to determine whether it will "induce" unwanted mutations. I'd be very surprised to learn that the FDA looks at potential vaccine/evolutionary relationships at all (obviously they wouldn't look at whether the vaccine "induces" mutations, because that does not happen), and the
CDC's own explanation of how a vaccine gets tested and approved seems to indicate that the main criteria for approval are (as should be obvious) safety and efficacy. Though some future researcher might choose to study the ongoing effects of a vaccine on viral evolution, this isn't part of the FDA approval process (how could it be? It would delay approval by years, with no especially obvious point at which you could decide "ok, I guess the virus just isn't going to evolve that way, so we're good to go"), so raising the vax's "experimental"/unapproved status is all really just a red herring.
In conclusion, Libya is a land of contrasts, and also yes, it is still entirely appropriate to shame those who choose not to take the vax, and it's still extraordinarily irresponsible for a doctor like your friend to discourage vaccination.