@srope-
I think exempt activities really only deal with not-for-profit entities, in which case I don't even think they are really tested on the CPA exam (if they are I'm guessing it will not make-or-break your score). I don't know if you've ever filed a 990 tax return before, but they are quite tedious. It's been awhile since I've done one, but from what I remember basically, not-for-profit entities are required to have a certain amount of contributions in relation to their net assets, and anything in excess of that limit that is set aside and NOT used for charitable purposes is unrelated business income that can be taxed. In my experience, this doesn't normally happen too often. I don't really know what would fall under this category, but my guess would be a large donation that serves no use to the entity unless they were to turn around and sell it for a profit (i.e.: a donated building that cannot be used in the normal course of business so they sell it- I'm just guessing here though). I think your example above isn't really an example of unrelated business income because the public's use of the facility is still the normal course of business (both disabled and non-disabled are USING the gym).
The only other area I can think of is unrelated business income for other types of entities, in which case they would still claim that income on their tax return (I think..). The only difference is that you can't deduct expenses that aren't related to your business.
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