North Face, citing federal lawsuits that were filed in anticipation of Mr. Trump’s decision, said it was donating $100,000 to an education center for Bears Ears.

And the Canadian company Arc’teryx announced it would donate the net proceeds of its Nov. 28 post-Thanksgiving eCommerce sales in the United States to The Conservation Alliance and an additional $30,000 to the alliance’s Public Lands Defense Fund, which is challenging the legality of Mr. Trump’s move.

But the intersection of retailers and politics can be fraught. In January, L.L. Bean, the retailer known for its winter boots, faced a boycott from its liberal customers after Mr. Trump tweeted his thanks to a member of the Bean family who had donated to a political action committee that supported his presidential campaign.

Mr. Trump announced his decision to reduce the public lands during a speech at Utah’s State Capitol in Salt Lake City, undoing the designations of his Democratic predecessors. President Barack Obama made Bears Ears a monument in 2016, and President Bill Clinton classified Grand Staircase-Escalante in 1996, using the Antiquities Act, which allows presidents to set aside landmarks and “other objects of historic or scientific interest.”

“Some people think that the natural resources of Utah should be controlled by a small handful of very distant bureaucrats located in Washington,” Mr. Trump said. “And guess what? They’re wrong.”

On Tuesday Mr. Zinke, in a call with reporters, directly addressed Patagonia when asked to respond to the company’s assertion that the president had “stolen” people’s land.

“You mean Patagonia made in China?” he said. “This is an example of a special interest. … Not one square inch was stolen. The federal estate remains intact.”