I am sure when Kasich refers to Judeo-Christian values, he is speaking about basic values that most of us share, be we religious - or Godless, like myself. He might have said pluralistic, democratic values, under the rule of law impartially and fairly applied, but that's more complicated. Kasich is not a theocrat.
The thing about this is that if he had left out the phrase "Judeo-Christian" and gave it the same content no one would object all that strongly. Heck, the US has been doing that sort of thing for decades when we give out aid to places. The ideology we project is basically that of whoever is in power.