The basis of the opinion is the 14th amendment's equal protection of the law provision. The opinion holds that Proposition 8 does not serve any legitimate state interest and that it was only intended to disparage gay people.

Regarding your cousin's scenario, if either state applied its law against marriages within the 1st consangunity to all proposed marriages, then it would not be construed as violating equal protection. In addition, federal courts have generally allowed states wide latitude to apply their own policies despite Article IV's full faith and credit clause.