I used an umbrella on one WT hike and not for rain, rather for the never ending SUN!
Western Washington weather is tricky - while down low near the open water it is usually mild, in July and August we do get warm weather, more so in the mountains. In August one should expect mid 70's to even 100+ days. Add in altitude and that sun gets hot. As well, Mid July through mid September is when you least see rain. It doesn't rain often in August, though if it does it dumps! This past summer we had a week of miserable 100+ days and in the mountains it was stagnant. Yech!
On rain gear: when it does rain in summer it is often very cold and bitter. Rain pants or skirt will be appreciated if up high. The passes are not the issue on the WT (up and over them quickly), rather the long traverses up and down said passes, where the winds howl in storms. Down low in the forests you would have to deal with soggy trees and greenery soaking you.
What you also face is bugs if you come before mid August, so do be prepared.