President Reagan, bowing to political realities, will allow a popular plant-closing bill he strenuously opposed to become law without his veto, White House spokesman Marlin Fitzwater said Tuesday. "One of the president's guiding principles has been to reduce the federal intrusion of government into the lives of all Americans," Fitzwater said. " But the Congress has taken a step in the wrong direction by passing the plant-closing legislation," he declared. "Workers should be given as much notice as possible when a business is forced to resort to layoffs . . . but the federal government's mandate that all businesses" must give workers mandatory 60 days notice of a pending closure is not the right way, he said.