I read the first 3 links and then quit. Each of those is dependent on the vaccine actually reducing the spread of Covid, which it in practice has not.
From the first link:
Vaccinating a large portion of the population will reduce the overall number of infections. Reducing the number of infections reduces the opportunities the virus has to mutate into new variants.
The first part of that has not played out with Covid, so the conclusion is inapplicable.
From the second link:
Bollinger explained that variants are spreading quickly as new mutations develop because “unvaccinated people are getting infected and infecting unvaccinated people at a high rate.” More than 99.9% of all variant infections are from or to unvaccinated people, Bollinger said.
Only 1 in 1,000 new infections is a vaccinated person infecting another vaccinated person? LOL I don't buy that number for one second. Not even close to that number. That claim is laughable at best.
From the third link:
Variants may also emerge because people are immune to the older versions of the virus. That’s more likely to happen with viruses having higher mutation rates — like influenza.
“Any virus will keep trying to change, so it can continue to spread. With all vaccines, the more quickly people get vaccinated, the better. The slower vaccination happens, the higher the chance of having mutations in the virus and the appearance of more variants."
Well that seems rather contradictory. If you have more people immune to older versions of the virus (like the vaccine is supposed to do), and a higher mutation rate happens because of this, that would seem to support the idea that either vaccinated people cause more mutations, or that the vaccine doesn't create immunity from spread.