How are we to know? We cannot do the research ourselves. If the medical professionals and both cancer societies and the studies I've seen say no link between cancer and the vax, I don't know who else you turn to for different credible information. I know a lot of people who got cancer and some who died from fast aggressive forms long before COVID arrived.
We lost three family members and one good friend to the virus and only my sister, already with advanced congestive heart failure, was vaxxed. Others (certainly not all) our family and friends who were not vaxxed had long term residual effect--scarring of the lungs and other negatives from the virus. None of the vaxxed who got the virus report similar long range effects. I know my niece's oncologist was far more worried about the virus exacerbating her cancer.
And despite all the stuff reported out there, I'm guessing the large majority of my friends and family are now vaxxed and multiple boosted, and I don't know a one of them who reports any negative side effects from it in any way other than a day or two of mild discomfort which is normal.
Again I don't recommend or not recommend the vax--it should be a person's choice. And no mandates.