WASHINGTON—A blue Louis Vuitton-style bag advertised by a Chinese merchant for $200 caught Andrew Carlson’s eye as he scrolled Instagram. And he knew he could buy it without paying the 25% tariff that President Trump put on Chinese handbag imports in May.

Since 2016, up to $800 in foreign goods shipped to an individual shopper in the U.S. are exempt from tariffs that predated the recent trade wars. The exemption allows consumers to avoid the shipping charge or higher price that American retailers often apply to recover the…

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