This article is pure journalistic garbage--It's not even developed well enough  to establish which vaccines we're talking about, but a Kennedy descendant argues that vaccination in general, cause brain injury and autism?  Really?   
Which vaccines are we talking about?  Flu?  MMR? DPT? Chickenpox? Rabies? Tetanus?   
Maybe then, we can cut to the sweeping generalizations about whether Lefties or Righties and Dems or Repubs are for or against.  Silly.