Yes, the Kim Basinger-Alec Baldwin split is big news, but so is something else involving the Oscar-winning “L.A. Confidential” actress — in New York, at least. Her sandwich. Yes, at the Stage Deli, on 7th Ave. at 54th St., there is a Kim Basinger special, comprised of chicken and bacon between two slices of bread. And there’s the rub. Basinger, 47, is a strict vegetarian and vocal People for the Ethical Treatment of Animals activist, and she has voiced a protest against the bacon and chicken combo. But the proprietors of the deli, which has several plates named for celebrities, accuse Basinger of fowl play. Rather, foul. “Like we do with everybody,” the Stage’s manager Gil Kashkin told the New York Post, “we asked her what her favorite foods were, and she told us chicken and bacon.” PETA, acting on Basinger’s behalf, continues to insist otherwise.