Yes. Straight people are allowed to get marry so you can’t deny that same law or protection to same sex attracted people.
And we already ruled separate but equal was discriminatory.
Using Brown vs. Board of Education and the 14th Amendment as bases for any future decision regarding Obergefell, you would think that it would be an easy slam-dunk. When speaking of the "equality" of "legal union" between two homosexuals and a marriage between two heterosexuals...
Brown vs. Board of Education dictates that Separate but Equal Education is discriminatory (and yet it still happens through diversionary funding from inner-city schools to predominantly white neighborhoods), but I'd argue by extension, it should make other institutions the same, including marriage, which as we have established, is a legal procedure in the United States of America.
Secondly, the 14th Amendment is not and should not be up for debate. The language itself is clear as crystal, as frank as Frankenstein, as blunt as an atom bomb. If the argument is that the 14th Amendment was in regards to laws that were racially discriminatory, then why does it not spread to laws that are sexually and orientationally discriminatory? Because those things weren't at the forefront of the debate when the 14th Amendment passed? If states are attempting to (and have) passed laws that directly discriminate against minorities, like homosexuals and other LEGALLY PROTECTED CLASSES, then why does the 14th Amendment magically not protect them from the government? Because a 2000-year old book "implies" that it is a sin against their religion? The Bible is not a precedent for a code of ethics, for ethics have existed long before the Bible's codification in the 200 ADs. The Code of Hammurabi has existed a full millennia and 3 quarters before this book, and was based almost entirely on secular law. Corpus Juris Civilis, the greatest legal book in the world, was written as a secular basis on how law should not only be interpreted, but also how it should be applied. The Bible can not, and should not be the definitive factor in deciding what happens in a nation with hundreds of millions practicing different religions and with wholly different ideals. To do so would infringe on freedom of religion, as established by the 1st Amendment of the United States, therefore, laws dictated upon by the United States Congress, President, and Supreme Court must be based entirely within the realm of equal and fair secularism.
The 14th Amendment then makes it plain, Homosexuals, African-Americans, and Transgender people should be protected classes of the United States, and therefore, fall under the protection of said amendment. If they are not equally protected, then once again, the 14th Amendment doesn't work, and is thusly a dead and shallow work.