A mutation, generally, is less lethal than the original virus. If it needs a host to survive, why kill it, and may it be more reproductive, increasing it's number of individuals to ensure it's reproduction.
If a vaccine skills the original, deadlier virus, but not the non-lethal mutation, that may not be a bad thing, because it may act like a smallpox type vaccine that uses a milder form of the pathogen to develop immunity to the stronger form, which still may be circulating along with the milder mutations.
If we take the Israel situation, the argument that all new cases are in the vaccinated makes sense, since close to 90% of Israelis are vaccinated. Almost all patients would be vaccinated, regardless of the reason for hospitalization, so we're back to the situation questioning if the presence of the covid pathogen is the actual reason for the hospitalization or the repercussions of the hospitalization.
Bigger issue could be that covid is a bio-weapon, with different variants programmed for release to counter potential vaccine development.
That would mean the mutants aren't the issue as much as different, more virulent versions of the pathogen which are released on a timetable.