This hasn't been my experience at all. I moved to Seattle from Alabama (almost 10 years ago now), and openly tell people I'm from Alabama, and I've yet to feel discriminated against because of it. In fact, some people are a bit envious of property prices there. I think mostly they are just glad I'm not from California ;).
They like you just fine. You're not like "them". You're not like the racist, bigoted, regressive, backwards, ignorant, inbreds of people who still live in the South.
Most people out here can comprehend the concept that there are people in our country who conservative, religious, and smart. They'd shit themselves if they met someone who was conservative and smarter than they were. (This is where you insert a joke about if they're so smart then why are they conservative! hardy har har.)
I grew up in Seattle and still live there. If you voice any opinions that are not in a narrow band of the far left wing, they (including recent transplants) will attribute you holding that opinion to your place of origin, rather than listening to any justification you have for holding that opinion.
My girlfriend's company in Capitol Hill is super big on diversity. It's a huge part of their hiring process. They're about 50 to 60 people large. I asked her how many conservatives work there. Answer: zero.
Along some axes Seattle is very diverse. But along others not so much.
