There is a far greater risk that a little-known viral infection might cause cancer than that an mRNA vaccine could cause cancer.
A paper came out a few days ago - preliminary data from cell culture, but from an excellent highly regarded lab - showing that fragments of SARS-CoV-2 may be reverse transcribed from RNA into DNA (the presumption being that the RT comes from functional genes in LINE elements) and integrated into the host genome. If this is happening, it might lead to false positive PCR tests in recovered patients.
Paper here:
https://www.biorxiv.org/content/10.1101/2020.12.12.422516v1.full.pdf
Bits of foreign DNA inserted randomly into your genome? Now that’s when you might start thinking cancer. Not that there’s any basis for major concern from these very preliminary data. But just to highlight that there is far more potential for unexpected dire long term outcomes from an as-yet poorly understood viral infection than there is from the vaccines.