it might be that "moderate" regional actors, like egypt, who have been critical of the new regime in syria, which is clearly a fascist government, are concerned that they might destabilize their own countries. egypt doesn't align well in the normal islamic theocracy v democracy spectrum in the middle east. egypt is a totalitarian, mostly secular state that is most likely to be destabilized by islamists and would observe their rise in syria or palestine with extreme caution.
graham may be pulling somewhat of a cato in seeking to divide and conquer a little, and that's standard american policy, in a way that might escape trump or go over his head.
it is not in america's interest to have a strong islamist state in syria or to continue to allow the turks to devolve back into ottoman authoritarianism. if this is graham's way to get that across, i have to agree with him, which doesn't happen too often.
legislation with teeth to protect the kurds would apply to syria, turkey, iraq and iran.