Washington is not a good candidate for spreading Taoism because it has to build a forge for an engineer pretty soon, and we don't want to whip it because that hurts cottage growth. We definitely do not want to whip forge, then monastery, then missionaries. We don't really want to slow-build missionaries either, because working mines detracts from working cottages.
So I think Stone City is the place to be building missionaries. I'm not convinced we'd be in Organized Religion long enough to show a profit - we only show a profit in cities that already have Taoism that are building buildings, and only in those cities can we build Tao missionaries with or without needing a Tao monastery.
We do want Taoism in Washington, but not before we are running the religion plus Pacifism. Likewise GPfarm.
We do want Taoism in Trojan Horse for espionage, but I'm not sure that we get the espionage bonus without us running a state religion. I think the 15% bonus is for having our state religion in the target city. Is the 25% bonus for having the holy city of a religion present in the target city, or for having the holy city of our state religion present in the target city?
So there may be no rush at all to have it anywhere, until we are ready to adopt Taoism... if anywhere, Trojan Horse looks like the place that does have priority