This is a bit of a complex question, so bear with me.

Alright, so, I'm usually knowledgeable when it comes to this topic, but this one question has been bugging me for the longest time, and I can't seem to find the answer to it anywhere on the internet.
Making this simple as possible, I live in the state of Oregon where we pay no sales tax, but we pay an income tax. I often visit Washington state and I often buy things from Washington state. Washington is the opposite of Oregon on the tax spectrum. There's no state income tax there, but they do have the sales tax. Some places, I'll flash my Oregon I.D and I won't have to pay a sales tax, but other places, I DO have to pay a sales tax.
I asked my father about this, and according to him, I don't have to pay sales tax anywhere I go in Washington because of a Federal law that prevents excessive tax stacking, or something along those lines. I tried looking into that, but couldn't find a solid answer to that question either. I'm aware State and Federal are two separate entities, but powers override one another all the time & all that jazz. So, ultimately, I am asking:
As a visitor in Washington state as an Oregon resident who already pays an income tax, am I still required by law to pay a sales tax as well if the business says I have to?
A source for this information would be nice too. Thanks for your time!