In Obergefell v. Hodges, the Supreme Court held that there was a constitutional right to same-sex marriage. Does this automatically extend to divorce, or is it possible that the Supreme Court will need to rule on a case in the future where a state refused to grant a same-sex couple a divorce because state divorce law only covers opposite-sex couples?
The court said in Obergefell (emphasis mine):
Under the Constitution, same-sex couples seek in marriage the same legal treatment as opposite-sex couples, and it would disparage their choices and diminish their personhood to deny them this right.
If same-sex couples are to be given in marriage the "same legal treatment" as opposite-sex couples, the divorce process must also be the same.