. Under the U.S. Constitution, states must grant equal protection of law to all citizens.
That implies making civil marriage available to same-sex couples.
No. The first question is: Is it a discrimination of a citizen or of a couple? Even with gay marriage banned, all citizen still keep the same right to marry a opposite sex spouse.
But the more important thing is: equal protection does not apply when there is rational reason for the discrimination, e.g.: banning some mentally ill people from gun ownership has a rational reason and thus can not be considered a violation of the equal protection of law of mentally ill citizens.
This is a non-discriminatory practice, despite the fact that a lot of gun violence is committed by mentally healthy citizens and a lot of mentally ill citizens would not commit gun violence, even if they would be allowed to own a gun.
Most opponents of gay marriage argue that differences in procreation are the rational reason why same-sex relationships can be treated differently than opposite-sex relationships. And it is certainly true that the likelyhood of procreation differs a lot between these two groups.
When a person can't do something because of the shape of their genitals or the pretense or absence of a Y chromosome, ipso facto that's not equal treatment.
Or just biology. I'm pretty sure I can never get pregnant. I think it might be related to the shape of my genitals. I should sue the state.