While McReynolds' anti-Semitism is well documented, the story is false.
According to a 2015 essay by Franz Jantzen, one of the court's photographers, it was all a misunderstanding based on a letter that McReynolds sent to then-Chief Justice William Howard Taft.
McReynolds said he didn't want to "go through the bore of picture taking until there is a change in the court." He doesn't mention Brandeis at all.
And in fact, Jantzen says McReynolds "showed up for all 10 sittings during his tenure when the new group photograph was to be taken."
"At nine of these 10 sittings there was at least one Jewish justice on the court — first Brandeis, then Benjamin Cardozo, and Felix Frankfurter — and although the seating arrangement never called for him to sit beside a Jewish justice, at three of these sessions either Cardozo or Frankfurter stood directly behind him," Jantzen wrote.
Sources: Journal of Supreme Court History, The New York Times