The first step against mental institutions was by Kennedy who's family had bad experiences with the mental health system. Blaming this solely on Reagan is misguided. Reagan just went with the flow.
With respect to the Kennedy’s bad experience, are you referring to Rosemary’s involuntary commitment and subsequent lobotomy? That was pretty awful, was there something more?
No that's it. JFK held a vendetta against mental institutions. He signed legislation to rid the country of them and create community mental health centers which was the first step in deinstitutionalization.