I'm from Michigan, just spent 6 weeks in Washington, mostly in Oly, but around Seattle too.
I can tell you, Michigan cards are valid at every dispensary I visited, the only catch was, I brought for my Washington resident GF that has a medical card and was always able to 'pick up' for her.
Every dispensary and collective had me put her name down, some needed to see my passport too, some nothing, but all purchases were in agreement with buying for her or growing.
It seems like my Michigan caregiver card gave me full rights to buy and grow with the many people in the know I talked to.
Oly hemp fest was pretty happening the first day too.
Seattle was a madhouse though, I'm glad I stayed in Olympia, a pretty relaxed city all around, cheaper weed than Seattle too.