FYI this wasn't Target changing its policy. This was Washington lawmakers closing a tax loophole that was meant to help attract Oregon customers to Washington businesses located close to the Oregon border. Note that Oregon has a VERY high state income tax, Washington has NO state income tax.
Technically, customers from tax-exempt places (Oregon, Alaska, Alberta, Montana et al) can still submit a form with receipts once a year to Washington's revenue department requesting a PARTIAL refund of the sales tax, but it's time consuming. The change made news in Oregon a few weeks ago, so some of Oregon guests knew about it, but others Oregon and the other tax-exempt states/provinces were annoyed. We just told guests that state law now requires us to collect the tax, but they can go to the DOR website to learn how to apply via mail for a partial refund.
Although rare at our store, in Washington enrolled Indian tribe members can claim sales tax exemption at "off the reservation" stores. I've processed a few of those. I'm guessing that settlements between states and tribes, related to old tribal treaties, are why this sales tax exemption exists. Oddly, when non-Indians visit restaurants or stores located on tribal land, most tribes charge a "tribal sales tax" to non-tribal customers.
Another group which is still tax-exempt are foreign diplomats with appropriate US state dept ID. I've processed several of those for local consulates.