Here is a great site. It is complicated, but the topic is complicated.
The tl;dr of the situation, though, is that the protein spike produced by the mRNA does induce the evolution of a line of immune cells modified to fight it (just like the normal, natural immune response to any foreign protein) but it doesn’t effect other cells.
Here’s an analogy: DNA is a printing press. mRNA is a page of written instructions printed from that press. The ribosome is the construction worker handed those instructions. The mRNA vaccine means that you take pages of instructions printed on someone else’s press and hand them to the construction worker, who then builds the spike protein. But the page of written instructions do not and can not land of top of the printing press and modify it any more than a real piece of paper laid on top of a real printing press can rebuild it. The only situation in which the prospect isn’t transparently idiotic on its face is for people with no understanding of genetics.