Hi Jay, sorry about that. The damp weather brings them out.
The adhesives now available for hair systems allow you a high degree of freedom to do physical activity and sweat heavily. You can certainly go to the gym, run, swim, cycle etc. with no problems. The hold you get does weaken when you are hot and sweaty, but it is still strong enough - if someone were to grab your system and pull, it would still be like pulling a large address label off a plastic surface. Obviously people don't pull one another's hair like that in the real world.
A couple of caveats though. First, I personally would be uneasy doing an activity where I was sweating heavily and then there was the potential for actual contact with my head, such as wrestling or rugby or some martial arts. The system is not going to fall off, but if you were unlucky someone could rip the front hairline loose, which would be embarrassing. So I would only do those activities if I was wearing headgear to protect the system. Second, for waterskiing, where there is the possibility of falling and being dragged at speed through the water, I would always wear a bandana. I think waterskiing is about the most risky activity in a system.
If you are physically active I would highly recommend a lace system, because it is breathable and water permeable. The other main alternative - plastic membrane or "skin" - is not breathable, and far less comfortable if you sweat.
Hope this is helpful.