Even if they magically did cause cancer, it would take a whole lot more years for anyone to see a 75% rise in cancer cases.
That's the main problem, vaccines were rushed out without long term testing which understandably has people worried.
For people who were young and otherwise healthy the effects of COVID were generally minimal. Weighing up "risk of dying from COVID" vs "risk of long term side effects from minimally tested vaccine" some people made the choice not to take the vaccine, and why shouldn't they? That was their choice to make.
If in "a whole lot more years" there is proven a link between the vaccines and cancer, or other seriously negative side effects then who's going to have made the better choice?
There are a _LOT_ of things on the market today - food additives, medicines, etc which have various negative health effects, some of which are long term and serious.