A follow-up here...
There was even a time, many years ago, that I got a “Tax-ID-card” (can’t remember what it was called, though) — in order that, being an Oregonian, I would not have to pay sales tax in the state of Washington. It worked and whenver I showed it, I would not have to pay the sales tax.
But, that was a very long time ago, and I gave it up and figured it just wasn’t worth the continual hassle. I paid the sales taxes after that... :-)
If you go to any stores in SW WA, and announce up front at the checkout that you’re an Oregon resident, just showing your driver license, you’ll likely face no hassle in getting a tax-exempt purchase. The outlet malls in Centralia, WA routinely ask, as well. Often, the stores on the WA border lower prices a bit so that WA residents will shop there, rather than going to OR.