I'm living in Seattle. Can I obtain a Schengen visa in Vancouver, BC, specifically at the Italian Consulate?
Embassies and consulates almost always prefer you use the embassy or consulate of the country you’re a resident of. Even if there isn’t a legal restriction, they’re more familiar with the documentation you might provide.
Given that there is an honorary Italian consulate located in Seattle: https://www.embassypages.com/missions/embassy7356/
You may want to email both the San Francisco and Seattle consulates and ask for their advice because as @Giorgio notes, not all honorary consulates can handle all services.