Natural mRNA sequences tend to contain uracil, which the immune system is not a fan of (https://www.sciencedirect.com/science/article/pii/S152500161...). The innate immune system generally attacks extracellular mRNA because of this. The mRNA in vaccines are specially modified to bypass the immune system and be taken into cells, at which point they will be translated into spike proteins and be expressed on the cell’s surface. In conjunction with an adjuvant, the immune system will recognize this as a threat and begin producing antibodies.

It’s certainly possible that mRNAs could do harm: they could code for protein sequences that might disrupt cellular function, increase cancer risk (e.g. by disrupting DNA repair or even causing mutations), etc. The spike protein is none of these things - it just gets expressed on the cell’s surface - so the risk from the vaccine is low. And, crucially, once the mRNA runs out, no more protein will be produced: mRNAs are degraded after protein translation. This serves to generally limit the amount of lasting impact that an mRNA vaccine could possibly have.