Hey all... My wife, son, and I just finished our hike. We started Tuesday (6/19) and summited from Trail Camp on Wednesday (6/20). The switchbacks are clearing, but as noted, there are few snowy/icy spots that need a little caution, but aren't too scary for most hikers. I would recommend taking microspikes for the next couple weeks, since those snowy/icy spots are tramped in solid, and not a lot of sunlight hitting them.
Oh, and if the rangers at the permit desk pull out the photo posted above of the helmeted kid clinging to the snow, and tell you that the Chute is the preferred route - don't believe them. I didn't see a single person ascend or descend the Chute on our trip.
The cable section is mostly clear (a dry path downhill of the snow, but uphill of the cables). Two to three switchback sections are being bypassed, which makes for a little bit of scrambling, but not too difficult. It's unstable ground though, so I found these spots the most precarious. Careful scrambling up these as you might send a bowling ball-sized stone down on your climbing partner.
There are two straight-line sections (photo posted earlier by someone else) with one of them being right before Trail Crest. These spots will probably remain for a while, but aren't difficult with microspikes and hiking poles. There is one funky path that's been created at the western edge of the last section that takes you up and over a muddy spot. Be careful here as you're probably so focused on the snowy stuff and might forget the muddy stuff.
Hope that helps! Good luck to all, and thanks to those prior that helped us out with important info!
If I can get this to work right, here are some shots looking west through the cable section on Wednesday, June 20th (6am ish)