I've heard from a few folks that they've started checking IDs at the Banneker Rec Center pool at Georgia and Euclid to make sure folks are DC residents. I've never been checked there, even after they supposedly started checking (I usually just immediately turn right and go to the pool) but beware!
Not sure if bringing a voter registration card or something with your address on it would help, but I'm going to try that -- I don't have a DC license. However, the DPR pool fee page just says "DC resident" and doesn't say anything about DC driver's licenses.
If you aren't a DC resident, it's $4 for adults.
UPDATE: A commenter says his library card works, so I would assume voter registration would work too. He says a piece of mail should work.
David Hockney painting not of the Banneker pool