For decades, America and much of the developed world threw their used plastic bottles, soda cans and junk mail in one bin. The trash industry then shipped much of that thousands of miles to China, the world’s biggest consumer of scrap material, to be sorted and turned into new products.

That changed last year when China banned imports of mixed paper and plastic and heavily restricted other scrap. Beijing said it wants to stimulate domestic garbage collection and end the flow of foreign trash it sees as an environmental and...