Zero. Cancer is not caused by the immune system functioning the way it evolved to function.
Whether or not you have received a vaccine, your immune system is busy defending your body against potential pathogens every single day. It is constantly making B and T cells to fight off pathogens, because unless you are a "bubble boy" who must live in a sterile environment due to complete absence of immune system, you encounter pathogens every day.
Cancer can be caused by exposure to some chemicals or pathogens that enter the cell. In either case, they disrupt cell function and/or damage the DNA (which permanently disrupts cell function). Cancer can also be caused by spontaneous DNA mutations (i.e. damage) in cells that the normal DNA repair mechanisms fail to correct.
I didn't say it was caused by immune functioning; I meant that it was facilitated by the immune system being weakened or diverted. There is a limit to how much it can handle at any one time; that's clearly been understood for quite some time.