It really depends on what your definition of “safe” is. The vaccines have stated side effects, some of which can severe. The side effects are relatively rare, but non-zero.
The other component is time. We’ve proven that the vaccine is mostly safe…for at least a year out. After that, we have no data.
You don’t have to look that far back to find things that were deemed safe at one time have disastrous consequences years down the line. Cigarettes, asbestos, etc.