How safe are anti-rejection meds?

Safer than Rejection. All medicines have side effects. It's the job of the transplant clinic to find the right cocktail for each patient which will prevent rejection with minimal side-effects. Because most patients are on combination therapy, there is a great deal of art as well as science which goes into finding the best combination of drugs.
Relatively Safe. The anti-rejections medications used today have been taken by patients for 20 years or more. However, they all have side effects of some sort, and they increase the chances of infections and possibly cancers down the road. They are needed to keep the transplanted organ working, and these side effects need to be balanced with the survival advantage that the transplanted organ provides.