That was a ruling that anti-miscegenation laws violated the Equal Protection Clause because they discriminated on race. The same cannot be said for gay marriage. In 2003, the Supreme Court ruled on
Lawrence v. Texas, which concerned sodomy laws. The Court ruled that mere moral disapproval of a group cannot be the basis for a law. In her concurring opinion, Justice O'Connor (at that time, one of the Court's moderates) indicated her belief that there could be constitutional reasons for limiting marriage to heterosexuals:
That this law as applied to private, consensual conduct is unconstitutional under the Equal Protection Clause does not mean that other laws distinguishing between heterosexuals and homosexuals would similarly fail under rational basis review. Texas cannot assert any legitimate state interest here, such as national security or preserving the traditional institution of marriage. Unlike the moral disapproval of same-sex relations—the asserted state interest in this case— other reasons exist to promote the institution of marriage beyond mere moral disapproval of an excluded group.
539 U.S. 558 (2003)
The best chance of legalizing gay marriages is to do it through state legislatures and statewide constitutional referenda. This is a political issue, not an issue that should be taken to the courts.