(FORTUNE Magazine) – * The ad, playing on local Washington, D.C., television stations, opens with a drawing of a family outside their house and the voice of a little girl saying: ''Right now, we can't protect ourselves from nuclear weapons and that's why the President wants to build a peace shield.'' As she speaks, a dome is drawn over the house, a satellite zaps incoming missiles above the dome, and a rainbow appears. Sponsored by the conservative Coalition for the Strategic Defense Initiative, the commercial is the latest salvo in the fight over the Administration's proposed Strategic Defense Initiative, or Star Wars. The coalition is trying to raise $1.7 million to air the ad in 20 major markets before President Reagan's summit meeting with Soviet leader Mikhail Gorbachev. As expected, opponents take quite a different view. The suggestion that the U.S. could build an attack-proof ''dome'' is misleading, says Howard Ris, executive director of the Union of Concerned Scientists, which ran its own anti-SDI TV and newspaper ads earlier this year. The union's own message: ''The heavens are for wonder, not for war.'' Promoters of controversial causes like to make their pitch on television. But money alone is not always enough. Many broadcast executives are wary of what they call ''advocacy'' advertising because they worry about skewing the debate on controversial issues. ''If we opened air time up for sale, it would be totally unbalanced by people who have the money,'' says Carl Trunk, an attorney for NBC, which rejects most advocacy ads. Some broadcasters say they're restrained by the Federal Communications Commission's fairness doctrine, which requires a balanced airing of controversial issues, but others including NBC, ABC, and many local stations accept some advocacy ads. Several organizations and companies, including CBS and Gannett, are asking a federal court to declare the doctrine unconstitutional. They argue that the increasingly deregulated broadcasting business provides enough diversity on air to guarantee a full spectrum of opinion. The FCC agrees with their point of view but says it will continue to enforce the doctrine until the law is changed.