Are you confused because you assume the "moral core" refers to the morality of adultery vs Trump's comments about "grabbing a woman in the p***y"?? It isn't.  That used to be a Conservative issue, until it no longer was. Progressives and liberals don't care about adultery,"perversion", "lewdness", etc.,  just about respect and consent.

It is the morality of sexual aggression (grabbing) and general indifference to women's issues, vs a feminist agenda.