This article in the Brooklyn Daily Eagle describes what happened, and while it tries hard to be as liberal as one could expect a newspaper to be in 1877, it ends up adding its own slightly more subtle anti-semitism to its analysis of the situation.
The newspaper, while disagreeing with Hilton's logic that Jews were uncivil, ends up siding with Hilton that if Israelites cause the Christians to be unhappy, then it is proper for them to be banned - as unfortunate as that may be.
The subtext in this and all similar articles from the time period is that Jews are not Americans, that they are at best some sort of exotic aliens with different manners and habits, but in no way would they be included in the same circle of coworkers or friends of the reporters.
Hilton expanded on his bigoted logic, saying that he had no problem with Hebrews (meaning Sephardic Jews) but he disliked "Jews", meaning Ashkenazic Jews like Seligman:
This was followed two years later by banning of Jews in a hotel in Coney Island, which received a great deal of coverage in the Eagle, including interviews with society ladies who agreed with the ban, rabbis who disagreed, and a lawyer who felt that the ban might not be technically illegal because summer beach hotels might not be considered "hotels" in the legal sense.
Editorial cartoonists at the time evidently enjoyed lampooning Jews. Harper's had an article that was supposedly against the ban, but the cartoonist seemed to think otherwise:
(This Harper's article is mistaken that Hilton and the Coney Island manager started an organization called "The American Society for the Suppression of the Jews." It appears that this was part of a satirical article printed in a Jewish newspaper about the incidents at the time.)
Another cartoonist, Puck, had his own solution to the problem:
Did Hilton's bigoted business decision pay off? Apparently not, according to this article from 1883. Hilton is sarcastically described as a "genius" in so thoroughly managing to ruin a beautiful hotel that was run profitably and successfully for decades before he became manager:
And how did the Jews react to this banishment? By beating Hilton at his own game. This article from ten years after the initial banning shows that Jews took Puck's tongue-in-cheek advice and ended up buying many hotels as well as presumably ruining Saratoga with their uncivilized presence. The article also relishes the possibility that a Jew might even buy the Grand Union and kick Hilton out.
That did not ever happen, and Judge Hilton died in the late 1890s, but not until after enduring the embarrassment of his son carrying on publicly with a mistress, a comic opera singer.
Discrimination against Jews in hotels continued, however, with a similar case in Providence and a hotel owned by the ex-governor of Rhode Island in 1897. The "Hebrew" sued for $50,000 in damages, but I could not find out the outcome of the case.