MAGDEBURG, Germany—The night after Donald Trump won the presidency, hundreds of backers of an anti-immigrant party whose success has shaken German politics gathered in the biting cold in this eastern German city and celebrated a new reality.

“Bravo, Mr. Trump, you get it!” state party leader André Poggenburg shouted from the stage last Wednesday, framed by the dark hulk of a 500-year-old Gothic cathedral. “Today, I must say, it is truer than ever: Merkel must go!”

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