NPR
Edward Schumacher-Matos responds to a listener's complaint by acknowledging that it doesn't make sense to label obstetricians who perform abortions as "abortion doctors," as a recent story did. "We don't say a physician is an STD doctor. Or a child-birth doctor. Or a breast-exam doctor," Schumacher-Matos writes. He found four uses of "abortion clinic" on-air or in headlines -- including once by him -- although NPR's style guide says not to use that term or "abortion doctor." He concludes:

Labels carry consequences. It would be too much to say that media usage of 'abortion doctor' was behind the murder of [Dr. George] Tiller. But the label certainly channels hostility against doctors who do the operation. ... The media's responsibility is to be accurate in framing an issue in all its complexity.

A quick Google News search indicates that the term isn't widely used in media. The Associated Press stylebook doesn't prohibit the term, although it tells journalists to "avoid abortionist, which connotes a person who performs clandestine abortions." || Related: Jay Rosen calls NPR abortion report worst form of 'he said, she said' journalism | The war of words and how we come to label Jared Loughner an ‘assassin