Responding to the criticism that judges would simply not interpret the ERA in this manner (similarly to how they haven't--yet--interpreted the 14th Amendment or the Civil Rights Act as barring affirmative action), Somin argues that the times have changed on the Supreme Court and progressives can no longer count on liberal majorities to establish precedents and interpretations in their favor on these issues.
This argument is not wholly implausible, but it ignores the massive differences between the judiciary today and that of the 1960s and 70s which created the dominant interpretations of the Civil Rights Act. At that time, the judiciary was overwhelmingly liberal and nontextualist. As a result, they were willing to deviate from the text to reach liberal results, especially at a time when Congress and the president largely approved of their objectives (as did even Republican President Richard Nixon, who supported affirmative action). Today, the judiciary is largely made up of judges appointed by conservative Republican presidents Reagan, Bush I, and Bush II, all of whom tried hard to pick judges with strong conservative credentials and (to a lesser extent) textualist approaches to constitutional and statutory interpretation. For example, almost 60% of today's federal court of appeals judges were appointed by conservative Republican presidents. With the replacement of Justice O'Connor (who waffled on the issue) by Justice Alito, the Supreme Court also has a majority hostile to affirmative action. And today's presidency is often held by conservative Republicans. Congress, even under the Democrats, is unlikely to have the kind of strong liberal majority that existed in the 60s and 70s.
What Somin doesn't mention, however, is that these conservative judges often at least nominally claim to adhere to originalism, not just textualism. And it is beyond clear that liberals do not intend the ERA to be interpreted in a manner that would preclude favored liberal policies. Indeed, the tone of Somin and Volokh's posts seems premised on this point--that liberals giddily pushing for passage of the ERA don't know what they're getting into (and certainly don't intend to live in a world where the aforementioned policies are deemed unconstitutional). While Volokh and Somin focus on the plain text itself (and agree that their interpretations are certainly plausible ones), the scholarship on the ERA (especially in recent years when it has seemed all but dead) has come primarily from the feminist left, which has created a paper trail that points rather strongly in the direction of an ERA not meant to embody an anti-differentiation principle (which is how Somin and Volokh read it).
So we are faced with an interesting conundrum for conservative judges nominally tied to originalism. The original intent, meaning, and understanding of this amendment almost has to be read in accordance with the scholarship that has been its primary exposition over the past 20 years or so. This scholarship embodies not just liberal, but relatively radical leftist positions on the relationship of law to subordination--positions that I'm a fan of, but conservatives tend to rail against with wild abandon.
Personally, I'm in agreement with Somin that conservative judges political opposition to many of these liberal policies will guide their interpretations, and originalist rhetoric will be co-opted or subsumed to that end. If so, that should drive a pretty large stake through the heart of the claim that originalism is a more "objective" philosophy of judicial interpretation--as opposed to just another guise by which judges install their preferences into law.