Earlier today, the Supreme Court struck down a Massachusetts law creating a 35 foot buffer zone around abortion clinics that protestors have to stay away from. Pro-choice groups unhappy with the decision have noted that the Justices themselves recognize the value of a little buffer zone and have in fact created a much larger one outside their own workplace.
Legally speaking, it's not clear that the Supreme Court's buffer is constitutional either.
In the 1983 case of United States v Grace, the Supreme Court actually struck down a law that banned demonstrations on the sidewalk outside the Court. In the Grace case, using language that was cited in the abortion decision, the Court held that public ways and sidewalks occupy a "special position in terms of First Amendment protection" and the government's ability to restrict speech in such locations is "very limited."
The more recent regulations, however, target not the sidewalk but the plaza laying between the Court's entrance and the sidewalk. Even so, in 2013 Federal District Court Judge Beryl Howell struck down the rules against protesting in the plaza, citing the Grace decision. However, rather than react to the decision by rescinding the rule, the Marshall of the United States Supreme Court issued a new version of the rule specifically citing conduct that "is reasonably likely to draw a crowd or onlookers" as the prohibited activity, banned "to maintain suitable order and decorum within the Supreme Court building and grounds." The new regulation also specifically exempts "the perimeter sidewalk" from the scope of the ban, in an apparent effort to distinguish the rule from what was struck down in Grace.
The new rule has not yet been litigated, and Howell's decision was not appealed so the Supreme Court itself has not yet had the chance to rule on the legality of the Supreme Court's own regulation. Consequently, no precise legal rationale for why the sidewalk/plaza distinction matters or the constitutional relevance of "decorum" has yet been offered.