At first blush, a case now before the U.S. Court of Appeals for the Ninth Circuit appears downright raunchy, brought by a Los Angeles studio whose films have titles like “Bedside Brat,” and “Sex in Dangerous Places.”

But the appeal, by Vivid Entertain­ment LLC, raises an intriguing constitutional issue: How far does the First Amendment go in protecting the free-speech rights of actors who have sex with each other in movies?