The problem with an American state being "Jewish" is that you would need some major and fundamental changes in the US Constitution. What prevents non-Jews from moving in, or Jews moving out? The reason it "worked" in Yiddish Policeman's Union is because the refugees were settled in a region that was remote, very scantily populated and a territory not a state. Additionally the Jews were sort of like the "DACA" kids OTL, allowed to stay there but not given immigrant status but residence permits that could be revoked at any time and also only good for Alaska. In the 1940s the bureaucracy to manage/enforce this, in the 1800s no way - you can't surround Montana with a "wall".
Utah is still majority Mormon after 170 years, so I imagine it'd just be a matter of getting the ball rolling.
Wyoming isn't that different from the Pale climate-wise, and if a bunch of Jewish intellectuals devoted to the cause opt to set up a university of repute in Wyoming and some religious leaders set up yeshivas that attract folks from all over, I think the place could stay Jewish.
Plus, who doesn't like the idea of Jewish cowboys?