A brief response...
Thomas and Scalia do not leave behind their originalist/textualist jurisprudence completely when they deal with EP cases. A simple review of their opinions would make this clear. See, e.g. United States v. Virginia (Scalia, dissenting).
Instead of a pure originalist bent, Scalia and Thomas have in many of the race cases adopted a sort of "principled originalism." The main principle embodied in the EP Clause is that we are to be treated as individuals, and that "we are just one race here. It is American." This was the view taken by John Marshall Harlan in Plessy v. Ferguson, and it is the notion of the color-blind constitution, which arguably can be defended upon originalist grounds, which infuses the jurisprudence of Scalia and Thomas on cases involving race.
Furthermore, the race cases provide a little insight into the subtle, yet distinct, difference between Scalia, always a positivist, and Thomas, who certainly believes in some type of natural law. Thomas consistently writes about the Declaration of Independence in his opinions on race, and seems to think that it was the principle of "We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty, and the pursuit of Happiness" which was lifeblood of the 14th Amendment. Take for instance his opinion in Grutter v. Bollinger:
For the immediate future, however, the majority has placed its imprimatur on a practice that can only weaken the principle of equality embodied in the Declaration of Independence and the Equal Protection Clause. "Our Constitution is color-blind, and neither knows nor tolerates classes among citizens." Plessy v. Ferguson, 163 U. S. 537, 559 (1896) (Harlan, J., dissenting). It has been nearly 140 years since Frederick Douglass asked the intellectual ancestors of the Law School to "[d]o nothing with us!" and the Nation adopted the Fourteenth Amendment. Now we must wait another 25 years to see this principle of equality vindicated. I therefore respectfully dissent from the remainder of the Court's opinion and the judgment.In the end, Scalia and Thomas cling to their originalist philosophies in the realm of the EP clause. While they do not always inquire into what was meant by those who drafted the amendment, and how was it received at that time, they very often do attempt these inquiries. Furthermore, even when they stray from a strict originalist view, they do so with a guidepost, with a shining principle infused by the original meaning which will aid them in attempting to do the best for the Constitution, for its original meaning, and for democracy. With at least a principle, they attempt to restrain the range of arbitrary judging; sometimes, pragmatic results may follow, often they will not, and that is because their principle taken from the Constitution precludes such a pragmatic result. Indeed Publius, the Brown question is the most difficult one for an originalist, and we will likely never find an adequate answer. That there is no answer does not mean we have descended into a nihilistic, pragmatic sort of judging; originalists must hold true to a principle which we see emanating from the text and meaning, and it is that principle which will guide us through.