It's not the same. In that case baking thing, the customers volunteered information about themselves and tried to force expression from another human the said person was uncomfortable with, thus violating said person's right to pursue happiness and liberty to choose who they engage in a contract with.

In the cases of vaccines, some businesses may try to require that a person have a permenant change to his body that cannot be undone in order to engage in a contractual relationship, thus interfering in their right to self determination and pursuit of happiness.