I'm a cis male, so I can't speak from the perspective of an LGBTQ+ person, just an ally. I definitely want to echo that Eastern WA (east of the Cascades) is much more conservative than western WA. As someone who lives in Spokane and moved from the west side of the state, I hear can be a better place, but frankly it's relative to eastern WA and Idaho. Spokane is a short drive (~30 minutes or so) to Idaho, and even less-so to its counterpart Spokane Valley. Even then, it's a stark contrast between north Spokane city and south Spokane city.

Puget Sound, specifically King county, will be the best place in my opinion for Washington. The greater Seattle metro and i5 corridor is probably the right place to start looking. Keep in mind the further from Seattle and Capitol Hill you go, the more pockets of right-wing you find.