FWIW, I always get my shots. For children, especially the very young (infants and toddlers) there is concern about vaccines interfering with the development of their natural immunity system and/or too many shots at once having a chance of causing health problems, but there is zero evidence of a link between vaccines and autism.
No doubt autism is on the rise and it's cause is disturbing. I've seen various theories on it including the overuse of sonograms on fetuses where the high frequency sound might be damaging delicate growing brains. We live in a society where trace amounts of pesticides and preservatives will show up in the bodies of all citizens. Another factor is increased awareness. Autism could have gone undiagnosed in many children decades ago but now is being identified and treatment applied. I do not believe the latter accounts for the entire increase but it is still a factor.