Virginia Attorney General Ken Cuccinelli, who has been engaging one culture-war issue after another since he came into office, says he doesn't think the 14th Amendment grants equal protection to gays and lesbians, arguing that "frankly, the category of sexual orientation would never have been contemplated by the people who wrote and voted for and passed the 14th Amendment.”
Igor Volksy explains that there's something called "precedent" involved here:
In 1996’s Romer v. Evans the court ruled that a Colorado law called Amendment 2, which rescinded recently anti-discrimination measures, violated the 14th Amendment’s equal protection clause because animus towards a certain group of people does not constitute “a legitimate governmental purpose.”
There are some very smart originalists. But I'm actually convinced that the reason it appeals to some people is that they think they don't have to read as much.