I've been pondering the fundamental difference between a good ME activity program and GET and I think I've got it. GET is all bassackwards, as usual. It says if you continue to exercise, you'll get better. A good ME activity program says, if you get better, you can do a little more. GET inverts the cause and effect.
When good ME activity programs do recommend actual strength exercise, it's usually a very specific kind.
Some suggest (if you are able) training your low level anaerobic (ATP-CP-phosphagen) metabolism to carry more of the load since aerobic glycolysis appears to be crapped out. Since low level anaerobic metabolism only lasts a couple of minutes before it needs replenishing, we have to do < 2 minutes of exercise, then rest. Lather, rinse, repeat.
This should apply to ADLs as well, but try cleaning the bathroom <2 minutes at a time with 2-5 minute horizontal rest breaks.
I can't do it. I use some of my precious limited aerobic energy so I don't go mad.
If you can train the functioning low level anaerobic system to do more, you could become a bit more functional -- do more before hitting your upper level anaerobic metabolism (anaerobic glycolysis). In that sense, it could improve your QOL/functionality somewhat. It does jackshit for the root ME, but a little more functionality is usually a good thing. Because you're not using the more slowly replenishing aerobic metabolism, and certainly not anaerobic glycolysis, this small amount of exercise using the quickly replenishing, functioning low level anaerobic metabolism shouldn't (theoretically) take away from your limited energy stores. Theoretically.
It should be obvious that if you want to try this, start low and go slow applies. I do 30 seconds of exercise, then rest. Sometimes 60 seconds. I might work up to 2 minutes before rest. Maybe. We'll see. I'm not counting on it and I'm not pushing it.