Even if vaccines caused autism at the rates found in the fraudulent study that started this nonsense, it would still be the rational choice to vaccinate your children. The likelihood of a child dying due to not being vaccinated is higher than the likelihood that the vaccine would cause autism that was found by the (again, fraudulent) study.
Another interesting thing to note is that after the study was revealed to be fraudulent, the anti-vaxxer movement started talking less about vaccines causing autism and started focusing on other supposed problems with vaccinations - that they contain scary sounding chemicals, or that they contain a portion of the disease causing virus and are therefore likely to cause an outbreak or that they somehow prevent the "natural" development of the immune system, etc. Anytime you find yourself defending a belief that was founded on bad evidence (i.e. a fraudulent study by a later discredited scientist) with new evidence that conveniently seems to justify the exact position you came to on bad evidence, you need to look very carefully and honestly at your reasoning because it's far more likely that you're rationalizing a false belief than that you came to a true belief based on bad evidence.