Reports abound of higher than usual crowds. But I've had three trips and each have found a good deal of solitude.
Late May - base camped Cherokee. While Sawbill and N. Temp were packed, there were plenty of open sites on Cherokee.
June - Malberg / Makwa / Boulder. Malberg was busy, but we had Makwa and Boulder to ourselves for 2 nights apiece. Saw very few other cancers in that area.
Last week - Clearwater Loop. Only saw 2 kayaks on Clearwater, otherwise we were alone from Clearwater to E. Pike. Saw just a couple parties from E. Pike to Pine. Easily found a gorgeous site on Caribou. Could have had the site on Little Caribou if we'd been willing to wait an hour.

Are we just lucky? Did we make the right sacrifices to the campsite gods? We'll find out next week on Wood Lake.

I have taken two trips so far. Mixed bag in terms of crowds.

First trip June 28-July 5

Bower Trout through Brule, the Cone Lakes into Davis, then east to Horseshoe and back down to Ram Lake. Every lake had sites open, except Horseshoe and one opened up just as I paddled into sight. But then multiple groups came through later looking for a site. I got reports that Winchell was full the night I stayed on Omega so 2 groups came to Omega looking and found a site. Many of the lakes I chose to stay on, I had to myself (Bower Trout, Vernon, Davis, and Little Trout). Generally lots of solitude, never met people on portages.

Second trip July 22-30
In at Cross Bay Lake then Frost River to Little Sag to Ogish. Then passed through Alpine, Seagull, and did long portage to Paulson on our way to Brandt. This trip was crowded! Got one of last sites on Long Island Lake and there were people everywhere. The day we did the Frost, there were 2-3 (couldn't tell if 2 of the canoes were together or not) other groups that came behind us hoping for the site on Afton. The next morning a solo canoe headed east on it bright and early.

Little Sag was pretty quiet, and Gabi and Agamok had sites. But Ogish was completely bursting at the seams as were Alpine and Seagull. We thought we would get Paulson to ourselves since it is hard to reach, but there was already 1 site taken, we grabbed the 2nd and 1 hour later a canoe came through hoping for a site and got stuck doing the 515 rod portage late in the afternoon after they took a rest break. Big crowds on the portages coming into Brandt from Round. We had to wait 15+ minutes for a group of 9 to pass through.

I was on Insula middle of June and thought it was less crowded than normal.

One impact of having so many newcomers is that it's possible many permits are being reserved but people may not going deep into the BWCA. Perhaps if you get past the crowds you have a lot of solitude and open sites. This is not based on facts, just a possible theory.

Went to Iron Lake in mid-July and saw only three other parties camping on the lake. Saw three or four other parties passing through in the five days we were on Iron. Definitely more people closer to the entry points than farther in.

Moose River to Iron in early June. It was busy... Saw people everywhere!
Taking another trip in mid/late August. Hoping for more solitude.

May opener - Brule circus with everyone's fishing britches on fire.
June - first week, cold and windy. EP 37 to malberg - hardly anyone. Beautiful trip. Weather maybe kept folks home?
July 4 - homer through Brule, quick overnighter. Sites hard to find but one on Pipe worked out. Lots of people, everyone chill and quiet and friendly
Aug - dropped son off at homer ep for a week exploring all around there with his buddy, meeting them at baker. I'll let you know how that went. I put in yesterday at Morgan, expecting crowds. It was very crowded. Morgan ep has a tiny lot that had three trucks crammed into it. Down the way a bit is the "overflow" which had a sedan and trailer, truck and trailer and another truck. I squeezed in on very end, single portaged into Morgan. All sites on vista taken (as expected), and all southern and eastern site on horseshoe taken, didn't explore nw. Turned around and headed back to Carl and lux. Lux taken. Carl open - any port in a storm, but I chose to return to the cabin. It was a long day, beautiful area. Trolled Vista but no other fishing. Did not see trash on portage or encounter loud rude people at all. I think it's as everyone says - high season, most folks staying close to ep, and it seems like the norm is a group of four or more.
For certain, it is crowded. But I think most folks are practing patience and just trying hard to get a little p and q like everyone else. Some dumb actors and bad apples, but it's not falling apart. Be flexible with your plan. Be patient and kind, especially to those serving you gas, nut goodie bars and cold six packs. It was super crowded last year as well.

Funny you should bring that up. I was just mentioning to my son that when you look at available permits thru mid August, you'll be hard pressed to find one in a lot of cases.

Stayed on Gabbro late May/Early June. Was worried about finding a campsite heading in. Only saw one other canoe in 3 days. Unbelievable.