Breast cancer cannot be caused by a COVID-19 vaccine.
This article mentions that immunocompromised people may require additional vaccines due to having a weakened immune system from processes such as chemotherapy.
The article attached explicit: "There’s no evidence linking COVID-19 vaccines to cancer. Both the U.S. National Cancer Institute and the American Cancer Society report there’s no information that COVID-19 vaccines cause cancer. There’s also no evidence that suggests the vaccine can make cancer grow or come back (recur)."
The claim that "The [COVID-19] vaccine may cause breast cancer" by the original poster is blatantly disproven by the attached article.
This is also disproven by a different article written by American Cancer Society linked below:
https://www.cancer.org/cancer/managing-cancer/coronavirus-covid-19-and-cancer/covid-19-vaccines-in-people-with-cancer.html