"(1) No vaccine manufacturer shall be liable in a civil action for damages arising from a vaccine-related injury or death associated with the administration of a vaccine after October 1, 1988, if the injury or death resulted from side effects that were unavoidable even though the vaccine was properly prepared and was accompanied by proper directions and warnings."
This is not new. This is not specific to mRNA vaccines. The simple math is that if you prepare a treatment and give it to 300 million people, 300 people with adverse reactions may make the entire endeavor unwise financially.
The National Vaccine Injury Compensation Program was established to partially resolve this [2]. They state:
"[The VICP] was created in the 1980s, after lawsuits against vaccine companies and health care providers threatened to cause vaccine shortages and reduce U.S. vaccination rates, which could have caused a resurgence of vaccine preventable diseases."
If you're interested in looking into the reasons why things are done a certain way, I suggest reading the law and understanding how historical events have led us to the (imperfect) system we have today.