This conversation gets confusing because "mutation" as a term is being used inappropriately (it's why I add scare quotes). I alluded to this already in my comment.

Actual mutations, as in DNA transcribing errors, will occur regardless of vaccines. It's an inevitable part of DNA replication. Such mutations can lead to evolution when faced with certain environmental factors such as a population bottleneck effect.

Vaccines, by way or increasing immune system response, can cause a population bottleneck effect and encourage evolution. We're seeing it with covid variants resistant to prior vaccines and immune responses.

by way of*

Noticed the typo too late to edit it. :V

The original "vaccines do NOT cause mutations" was playing the same semantic game, by replying to a comment (that was obviously referring to selection pressure from population bottlenecks) with the most obtuse interpretation of it.