Wanda confronts Ida with her Jewishness but that isn't Wanda's primary identity, either. Her judgeship represents a career on the skids; a decade earlier she was a state prosecutor, presumably conducting political purge trials, and she's still willing to use her office as a threat to uncooperative people. Ida, however, presumably sees Wanda as not so much Jewish or Communist as modern and secular. The climactic scenes come when Ida resolves literally to walk in Wanda's shoes and consummate an attraction to a progressive jazz musician. Ida's unburdened by Wanda's issues (guilt, alcoholism, etc.), but like Wanda, if less dramatically, she seems to opt out of modern life.
Ida chronicles a futile quest for authenticity. A reactionary reading of it might see her reversion to habit -- clothing, that is -- as a decision in favor of the Church as her true home, but the ambiguity of her Catholic identity is the starting point of the entire picture. If you accept that there's something essentially false about her faith -- so long as she didn't have a choice to embrace first her Jewish heritage and then Christianity -- you face the bleak conclusion that there is no "authentic" Polish identity anymore, or anymore than any nation could claim to have by the mid-20th century. In that context it makes more sense to see more ambiguity in the ending. Dressed in her habit again after her tryst, Ida walks briskly foward as the camera retreats. You might assume you know where she's going because of what she's wearing, but I think it's important that we don't see her destination, that the film leaves her still moving.
Pawlikowski, who has worked primarily in English, evokes the film's period with a rigorous monochrome style many viewers find reminiscent of Ingmar Bergman. He works with a pre-widescreen squarish frame in which Ida is often a small figure at the bottom or in a corner. He also employs a kind of retro-modernism in the jazzier scenes amid midcentury decor. In short, the director makes it as obvious as possible that his is an arthouse film, but he and his cinematographers make their pretentiousness often quite impressive. He gets the desired guilelessness from his amateur lead actress, while Agata Kulesza easily dominates the picture whenever Wanda's on screen. Ida is the sort of picture that will be more admired than enjoyed, but in its ambition and execution it does deserve some admiration.