"Public officials who address matters relating to their public office on personal accounts will run the risk that every action taken on that account will be state action subject to constitutional scrutiny," according to the filing.
The challenge may face an uphill battle. In the earlier ruling, Circuit Judge Barrington Parker noted that @RealDonaldTrump is "one of the White House's main vehicles" for official activity -- it's under scrutiny precisely because many of Trump's tweets are state actions. He "hereby ordered" companies to find alternatives to production in China on August 23rd while using his personal account, for example. If Trump was allowed to block critics of his policies on his personal account, other politicians could simply shift their announcements to personal accounts to avoid their responsibilities for civic interaction.
This lines up to a degree with a January ruling that an official's Facebook page is a public forum. As it is, there are calls for consistency across the aisle. Critics have sued Rep. Alexandria Ocasio-Cortez arguing that they, too, shouldn't be blocked on Twitter merely based on disagreements. While Trump may not be fond of seeing critics' tweets, the ruling could also ensure that rival politicians have to contend with online objectors of their own.