The assertion that American politics have shifted right is counter to most research. Since the 1994, the effect has been perhaps moderately left, with the most notable shift to polarization.
On the whole, when taking into account stated positions (votes, speeches, etc) Clinton is far from conservative. Of the remaining field, Kasich is actually the most ‘moderate’.
When no member of Congress works across the aisle, folks who do so, like Clinton and Kasich, seem like aliens to those firmly entrenched on either side of the barbell.