The scary thing is that it is the spike protein producing mRNA that is injected as a vaccine. This mRNA was specifically produced to be more stable than the naturally occurring version. MIT discovered that this means its more likely to transfer back into the cells DNA.
https://childrenshealthdefense.org/defender/science-mrna-vaccines-alter-dna/
Process — mRNA is not DNA. So, if a person’s DNA was going to be altered, the RNA would have to be made into DNA. This would require an enzyme called reverse transcriptase. People do not have this enzyme, and only some viruses do. Coronaviruses are not one of them. Viruses in the Coronaviridae family have single-stranded RNA, known as “positive-sense” RNA. This means when coronaviruses enter the cytoplasm, they do not need to be transcribed. Proteins can be made directly from the virus’s positive-sense RNA. In this manner, the mRNA vaccine acts the same way, delivering mRNA to the cytoplasm for direct translation into protein.
https://www.chop.edu/news/news-views-3-questions-you-will-get-about-new-mrna-vaccines