Unlike any previous Republican presidential nominee, Donald Trump is casting himself as a champion of gay rights as he seeks to outflank Democrat Hillary Clinton’s response to the massacre at an Orlando nightclub.

Mr. Trump suggests he is a better friend to the gay community than Mrs. Clinton because his proposed ban on Muslim immigrants would block antigay Islamic extremists. The suspected shooter at the gay nightclub was born in New York to Afghan immigrants, and investigators are probing reports he used gay dating services.

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