The San Francisco Chronicle OCTOBER 6, 1992, TUESDAY, FINAL EDITION Sinead's Surprise Stirs It Up JOHN CARMAN The NBC switchboard was still laboring to keep up with viewer protests yesterday in response to singer Sinead O'Connor's making a jackass of herself on ''Saturday Night Live.'' O'Connor concluded her a cappella version of the Bob Marley song ''War'' Saturday night by tearing in half a photo of Pope John Paul II, while exhorting the audience to ''fight the real enemy.'' It was a high-water mark in pretentiousness, surpassing her own performance earlier in the show in which O'Connor had a 40-member string section backing her on her first song. It was also tasteless and tactless, and NBC spokesman Curt Block said that as of noon yesterday, the network had logged 1,090 phone calls protesting the Irish singer's action. Block said the phone count was probably increased because two New York tabloids, the Daily News and the Post, ran front-page stories yesterday about the incident. Nor did it help that O'Connor wore a necklace adorned with a Star of David on the program. The Anti-Defamation League was quick yesterday with a statement condemning O'Connor for ''conveying hatred to a religious leader who has fostered international peace and understanding. . . . We were shocked to see Ms. O'Connor prominently wearing a Star of David, further adding to her irreverent behavior.'' O'Connor's song is a militant call for an end to racism and other forms of injustice. In dress rehearsal, Block said, she'd concluded it by ripping apart a photo of a child. She used a picture of the Pope for the live broadcast. By the way, at the close of Saturday's show, the regular cast members crowded around guest host Tim Robbins and virtually ignored O'Connor.