Is "When Harry Met Sally . . ." a Christmas movie? Is it a Jewish movie? Is it both?

We watched When Harry Met Sally . . . with our 15-year-old last night. They enjoyed it and now understand the source of many cultural references (low maintenance, singing in front of Ira, not fucking with Mr. Zero, "because of God," etc.) that have bounced through our house for years. Next up, I guess, is Casablanca. Until then, two questions:

First, is this a "Jewish" movie? I saw an academic talk years ago that argued this is another version of the "Jewish man's opposites-attract relationship with the strange non-Jewish woman" story. I have never bought it. The movie is "Jewish" in that the writer (Nora Ephron), director (Rob Reiner), and male lead (Billy Crystal) are Jewish--but that is true of many movies (running Hollywood has its benefits). The story is loosely based on Reiner's experiences reentering the dating scene following his divorce. Sally is not Jewish (we twice see her buying a Christmas tree--more on that below). But is Harry meant to be Jewish? The story never makes that explicit. He is based on Reiner and played by a Jewish actor presenting "typically Jewish" mannerisms and personality. Harry Burns is a Jewish name, I guess, but it is no Isaac Herschkopf. Perhaps it does tell the Jewish-man-chases-shiksa story, sanitized for a mainstream audience. On the other hand, if you kept everything the same as the original movie and put Tom Hanks in the male lead (i.e., if you made Sleepless in Seattle or You've Got Mail*), would we think of this as a "Jewish" movie?**

[*]  In You've Got Mail, the Hanks character is Joe Fox and the mammoth chain bookseller is Fox Books. The irony for people watching that movie in Philadelphia was that Fox Books is a multi-generational independent bookshop around the corner from a Barnes & Noble, and its founder was Joseph Fox, who was Jewish.

[**] On a third hand: Ephron claimed that she based Sally on on herself and her friends. So you could tell a different Jewish story by remaking the movie with Jesse Eisenberg and Lizzy Caplan.

Second and more controversially: Is it a Christmas movie? The current-day (non-flashback) story appears to cover roughly 16 months--they reunite in late summer/early fall and the story ends on New Year's one year later. They pass through two Christmas seasons--captured in two winter-and-Christmas-in-New-York musical montages set to Christmas standards and buying Christmas trees (for Sally, not for Harry, of course). The different tenor of the Christmas montages evokes the different stages and states of their relationship, although with limited dialogue. The "action" of the seasonal scenes occurs not on Christmas but at two New Year's Eve parties--is New Year's part of Christmas for Christmas Movie^TM purposes and should it be?