She was in High School when she "supported" Goldwater.
By her junior year in college she had left the part of her parents and was a solid Dem.

"...In her junior year, Rodham became a supporter of the antiwar presidential nomination campaign of Democrat Eugene McCarthy.[27] In early 1968, she was elected president of the Wellesley College Government Association and served through early 1969.[25][28] Following the assassination of Martin Luther King, Jr., Rodham organized a two-day student strike and worked with Wellesley's black students to recruit more black students and faculty.."

"...Rodham then entered Yale Law School. There she served on the editorial board of the Yale Review of Law and Social Action.[38] During her second year, she worked at the Yale Child Study Center,[39] learning about new research on early childhood brain development and working as a research assistant on the seminal work, Beyond the Best Interests of the Child (1973).[40][41] She also took on cases of child abuse at Yale–New Haven Hospital[40] and volunteered at New Haven Legal Services to provide free legal advice for the poor.[39] In the summer of 1970 she was awarded a grant to work at Marian Wright Edelman's Washington Research Project, where she was assigned to Senator Walter Mondale's Subcommittee on Migratory Labor. There she researched migrant workers' problems in housing, sanitation, health and education.[42] Edelman later became a significant mentor.[43] Rodham was recruited by political advisor Anne Wexler to work on the 1970 campaign of Connecticut U.S. Senate candidate Joseph Duffey, with Rodham later crediting Wexler with providing her first job in politics.[44]..."


"...Rodham began a year of postgraduate study on children and medicine at the Yale Child Study Center.[52] Her first scholarly article, "Children Under the Law", was published in the Harvard Educational Review in late 1973.[53] Discussing the new children's rights movement, it stated that "child citizens" were "powerless individuals"[54] and argued that children should not be considered equally incompetent from birth to attaining legal age, but that instead courts should presume competence except when there is evidence otherwise, on a case-by-case basis.[55] The article became frequently cited in the field.[56]..."

"...During her postgraduate study, Rodham served as staff attorney for Edelman's newly founded Children's Defense Fund in Cambridge, Massachusetts,[57] and as a consultant to the Carnegie Council on Children.[58] In 1974 she was a member of the impeachment inquiry staff in Washington, D.C., advising the House Committee on the Judiciary during the Watergate scandal.[59] Under the guidance of Chief Counsel John Doar and senior member Bernard Nussbaum,[40] Rodham helped research procedures of impeachment and the historical grounds and standards for impeachment.[59] The committee's work culminated in the resignation of President Richard Nixon in August 1974.[59]..."

It's wikipedia, but their sources are cited.
https://en.wikipedia.org/wiki/Hillary_Clinton