As a lawyer, could you explain how denying over 1,000 federal marriage benefits to same-sex couples would be offering them equal protection under the law?
Had they challenged benefits laws, that would change the equal protection analysis significantly. But in this lawsuit, given what they've actually challenged, the normal precedent would be to apply the rational basis test, and nothing stronger.
Again, i'll quote roberts, who quotes lawrence:
"In any event, the marriage laws at issue here do not violate the Equal Protection Clause, because distinguishing between opposite-sex and same-sex couples is rationally related to the States’ “legitimate state interest” in “preserving the traditional institution of marriage.”" Lawrence, 539 U. S., at 585.
(Now, you could argue this isn't a legitimate state interest, but that's a pretty resolved question at this point, and would require overruling about 200 years of precedent on the issue :P)
The majority doesn't even bother to argue otherwise.
Second, the vast majority of the opinion does not rest on any equal protection claim, and not even the majority takes that argument seriously on these facts given the above. In fact, the majority doesn't even explain how their argument that this is correct works. They don't even spend a paragraph explaining it, just make a conclusory statement.
So to answer your question, i don't claim what you are stating would in fact, be offering equal protection, but will point out
A. This isn't actually the case before the court
B. Resolving that case does not require declaring states must issue same sex marriage licenses. It would probably require that those validly marriage be given the same benefits. SCOTUS is supposed to go out of it's way to not resolve questions not before it, and when they do resolve questions, they generally resolve them in the least sweeping way possible.
So, I assume you're leaving Loving v. Virginia out of that figure? [1]
Loving v. Virginia was struck down because it sought to arbitrarily hinder this right. However, gay marriage is a very different issue, because it seeks to expand the right to more people.
I would also take issue with your framing of this case. I view gender as just as arbitrary a hindrance as race, especially given that the "Biblical definition of marriage" also dictates things like how one should treat their sex slaves. It's also worth noting that it was religious conservatives that were also raging against the decision in Loving v. Virginia, because it violated "traditional" notions of marriage.
So, what's the difference between an "arbitrary hindrance" and an "expansion of rights"? Who gets to decide? Which one is allowed, in your view?