I'm the guy [Bil Paul] who developed and researched the Sierra Cascades route and glad to answer your question about carrying a water filter. Most places, there are enough towns and campgrounds along the way for you to get your water supplied. The places where there aren't that many resupply and piped water points are North Cascades National Park in WA, the area around Mt. St. Helens (Pinchot National Forest) in WA, the area between Mt. Hood and Detroit Lakes in OR, the area south of Lake Isabella (before Techachapi) in southern CA, and perhaps Road S1 south of Julian -- I think it's also called the Sunrise Hwy.
Myself, I always carry a water filter on all tours as a matter of course. I carried one on my last tour along a portion of the Western Express route and never used it once, but still nice to have.
So there you have it. I hope that helps!