She can keep it real as she wants and she still has 2a rights. However since a key element of the job is both the appearance of and actual impartiality it's troubling for a judge to do so unless she wants that impartiality questioned later.
With the modern world we live in... instant communications... social media networks...
The entire concept of judicial impartiality is a fantasy of a bygone era when news from around the country took weeks / months to travel, and a bunch of old legal scholars could hold themselves up in study of the law and spend their time isolated from the political battles in the halls of Congress.
Today it is of the utmost impossibility for our SCOTUS not to be political. Impossible for them not to be in the literal thick of social upheaval. And for there to be just 9 of them means a GREAT deal of pressure is placed onto them, from all sides. All day, every day.
Our founder's concept for the Judicial branch has long since been dead, gone, and buried.