Off hand my first thoughts are (a) well it would make sense that the non-rapamycin-sensitive cancer cells would naturally be selected for - but that doesn't mean that your rates of cancer would be higher - and (b) how do you square this with the measured lower cancer rates in transplant patients on rapamycin?
My take, admittedly more research needed on my part, is that the cancer risk of anti rejection drugs is because the immune system would normally nuke some of these from orbit. However rapamycin works differently and doesn’t suppress the immune system so even with resistance developing the cancer risk would still be somewhere between lower and neutral.
https://pubmed.ncbi.nlm.nih.gov/21389767/
Disclaimer: The newer the article, the less reliable it is. There were well disguised garbage articles in the 2000's, but there are too many now.