The Leave No Trace principle of not hiking on a muddy trail doesn’t work well if you’re on a portage in the Boundary Waters or on a thru-hike on some extensive hiking trail. In the BWCA you will encounter wet portages and there usually isn’t an option to turn around unless you want to alter your route. What should you do when you encounter mud on a trail?
If you’re in the BWCA you have hopefully already given yourself permission to get your feet wet so a little bit of mud shouldn’t be a big deal. When you encounter a portage with mud on it then proceed with caution down the middle of the trail. Do not go around it because you’ll end up damaging plants and making the trail wider and more prone to erosion. You don’t want to create new trails that could possibly confuse other trekkers either. If there’s a down tree in the way then consider taking the time to move it or use your saw to cut it up if you can. If you can’t move the tree or cut it up then when you’re back in civilization let the USFS know about it. They may have crews in the area that can take care of it.