Think again. Justice Antonin Scalia (no longer a right-wing outlier on the Supreme Court but now a frequent part of a ruling majority) thinks the Constitution's equal protection clause does not prohibit discrimination against women (or, by extension, any number of other abused classes to which it has been applied.) You want to pass some anti-discrimination laws? Fine. Just don't look for the Constitution to protect you. The flip side, of course, reaches far more than women. Scalia's view means Congress and the states CAN pass laws discriminating against all manner of people, gay people first off.
All the more reason that Bernadette Cahill had a good idea when she wrote in our Big Ideas issue that Arkansas should move forward to ratify the Equal Rights Amendment.