"Public officials dealing with matters relating to their public office on personal accounts will run the risk that any action taken on that account will be a state action subject to constitutional control," according to the filing.
The challenge could face an uphill battle. In the previous sentence, circuit judge Barrington Parker noted that @RealDonaldTrump is "one of the main vehicles of the White House" for the official business – it is under investigation precisely because many of Trump's tweets we are state actions. He "ordered" companies to find alternatives to production in China on August 23 while using his personal account, for example, and incorrectly. If Trump were allowed to block critics of his policies on his personal account, other politicians could simply move their ads to personal accounts to avoid their responsibilities for civic interaction.
This is in line with the January ruling that an official's Facebook page is a public forum. As it is, there are requests for consistency throughout the corridor. Critics have sued the representative Alexandria Ocasio-Cortez claiming that they too should not be blocked on Twitter simply because of disagreements. While Trump might not like to see critics' tweets, the ruling could also ensure that rival politicians have to deal with their online objectors.