No one is suggesting any amendment of the sort.
In Brown v. Board of Education that the Supreme Court ruled that "separate but equal is not equal." So what does that mean here?
1. The government must recognize gay and straight marital relationships using the same word for both.
1a. If benefits provided by the government are to remain existing, the government must either use the word "marriage" to describe both straight and gay couples and issue Marriage Licenses to all couples or use the words "civil union" to describe both straight and gay couples and issue Civil Union Licenses to all couples.
1b. The government can also choose to recognize neither straight nor gay marriages and remove any benefits associated with marriage provided by the government and issue no licenses whatsoever. This is where we agree.
2. The government, if it is to recognize marriages in the equal manner described in 1a, must require private entities to treat all married couples, straight or gay, equally according to Brown v Board of Education.
2a. If the government does not recognize marriage at all, it need not require private entities do treat straight and gay couples equally.