No, but we have many other vaccines and some crackpot could make up some fake data claiming that vaccines cause cancer and that we never had all this cancer back in the "good old days" before vaccines were invented.

You mean when everyone was dead long before the cancer could've had a chance to kill them?

You're thinking much too logically; these people will either deny basic facts or base their opinion on something completely disproven, in order to cling to their opinion.