Heh, I was wondering who would be the first one to reference that law–it immediately appeared on right wing Twitter and sites like Breitbart, which is fairly common–people do something you don’t like, find some random law that maybe makes it illegal. (These same people of course ignore the potentially dozens of laws broken by things like the January 6th coup attempt.)
I don’t really think that law would prohibit protesting outside of Alito’s house. It is very narrowly constructed textually.
It pertains specifically to either impeding the administration of justice, or “influencing … the discharge of his duty.”
Impeding or interfering with the administration of justice is pretty tightly defined, so for example if they were trying to stop a judge or juror from being able to get through the crowd to go to the courthouse to fulfill their duties in a court hearing, that would be such a situation. None of these protests really seemed to be doing that.
The other aspect is “influence” them in the discharge of their duties. That is an intent based crime. If the police arrested a bunch of people on this charge, they would have to prove that the intent was to influence Alito’s discharge of his duties. A simple explanation that the protesters were simply there to express their displeasure, as per the First Amendment, would be difficult to overcome at trial–perhaps not impossible, particularly for people in the crowd who may have published their intent elsewhere, but out of the dozens or hundreds of people doing it, I imagine only a small handful will have done so.
Anything beyond a narrow reading or a narrow enforcement would raise significant first amendment concerns.