Since he was a Green Party candidate in the primaries, does “Republican district court judge” now mean he is from a Republican leaning district while “Republican District Court Judge” would mean he was a Republican himself? Do we now have to check for upper case and lower case letters? The propaganda media finds so many ways to mislead.
NY’s party system is... odd. You can be nominated by multiple parties, and if so you appear on the ballot multiple times (and your vote total is counted among all parties). A couple of years ago, several Republican judicial nominees (a personal friend of mine included) were part of a bit of a minor party coup after there was shenanigans with the Conservative party agreeing to nominate some Democrats for their line... several Republicans managed to get themselves nominated by the Green party.
So while he may have been in the Green party primary and one of its nominees, he was a Republican.
District Court is the court he was on.