Like the clandestine agents working for Tom Nook and examining every nook and cranny of your house at night with elite-forces levels of training, and the unknown agents the real mayor Isabelle references when discussing the assessment of your village (how else do these overseers know your village so well, and are updated on a daily basis?), Chrissy is another spy in this Aldous Huxley-style
Brave New World police state, but the catch is the naive mayor is meant to see through her disguise: she is a distraction to keep attention focused away from the real agents.
She's like the Invader Zim of the Irken Empire (picture him wearing that
old man "disguise", and the even worse one of his "dog" (shown in the same screen shot linked above)).