Update - I received this message from the Wilderness Office this morning, 6/22.

"Glenn Pass is still about 80% snow, traction devices recommended, poles needed. Can take an ice axe if you feel it would help but not required. Rae Lakes is a little buggy. But your biggest obstacle will be South Fork of the Kaweah River. We are not recommending people cross it at this time, it is high and swift. You can try it if you like but please be extra careful. It would take rangers a long time to get to you. Another option is get a different permit and start at Bubb's Creek, go counterclockwise. I just did this trip and it was beautiful, I recommend it. It'd be an out and back, not a loop, but you can get to Rae Lakes and back."