The WHO and the CDC are using the exact same safety protocol for mRNA as for any vaccine - they have speeded development up by risking money not lives.
The mRNA vaccines are very clean vaccines. They don't do anything to the cell DNA. They are instructions to make the spike of the protein, your body then fights off the spike and then the mRNA and the spike are gone and all that is left is the memory of how to fight the disease.
The spikes can't harm you as they can't infect by themselves, they need the virus attached to them- they don't have instructions needed to tell a cell to make more spikes. So once the original mRNA is gone and the spikes are gone there is nothing left except the memory of how to fight them.