The whole thing with the teacher is very clearly a tribute to Jack Kirby and his wife, bc the character is named Rachel Rozman & ... Rosalind Goldstein-Kirby was known as "Roz." Jack used to draw holiday cards featuring The Thing, made him from a neighborhood based on his childhood home & very clearly identified with him just a little bit more than other characters.
From the Hebrew text I could see on the siddurim in the shul, it seems to called "Beit Tefillah," literally "House of Prayer." It's so generic a name that it's practically called "The Church of Churchington Churchiness."
There is literally nothing "Zionist" about anything Jewish that shows up in the movie. It's all as New York Jewish as possible. Ben's rocky feet are planted right on Yancy Street. If anything, the movie is full of doykeit.
I wish it were more surprising that "something is visibly and simply Jewish, specifically American Ashkenazi Diaspora Jewish," is being called "Zionist propaganda," but.