All three of the national parks in Washington are now open for backpacking, though not necessarily every area, but most of them. But the method for getting permits is different. The biggest difference of for the Olympics, where many areas previously just required self-issue at the trailhead. That doesn't exist this year - everything in the Olympics is now reserved on reservation.gov, which means that all backcountry sites are effectively under quota. Rainier never had self-issue, but it had same-day permits at ranger stations, which was good if you lived nearby and were flexible. No such this year, there is a website for reserving permits between a week and a month ahead. North Cascades is still offering same day permits, but only from Marblemount, no other locations. But you may be able to call in if you aren't driving through Marblemount.
I usually visit a couple of these parks each year and I'm not sure how these changes will affect my plans. I also worry that with the covid spread picking up, that these parks may close again. Please everybody do everything you can to slow the spread so that everything that has opened, including business in our towns, do not have to close down again! Wearing a mask is not a political statement, and with something like 130,000 dead Americans, your best way to preserve your freedom overall is to stop or slow down the spread.