Why does Tobias Wolff depict the Jewish faith as something to hide in order to fit it with the privileged?

The prep school that the narrator attends, though unnamed, shares many of the features of elite educational institutions both then and now. The school is steeped in one form of snobbery or another. Most of those attending come from wealthy, privileged backgrounds. The narrator is an outsider on two levels: first, because he's a middle-class boy on a scholarship; and second, because he's a Jew, and anti-Semitism is a widely-held prejudice among both boys and masters alike.
Also, the narrator is somewhat confused in his own identity as his Jewishness has only recently been revealed to him, so he doesn't quite know where he fits in. Add to that the fact that his father is not only embarrassed about, but actively hostile towards, his own Jewish heritage, and it's not surprising that the narrator is rather reluctant to proclaim his religious faith openly.