I call this a plothole...
from what we've seen so far, the ANBU were guarding the villiage during the chunin 3rd exam, they looked for information and they're in charge of disposal of missing-nins....

that sound like the police for me, and seeing that Itachi was head of the ANBU, it even makes more sense...

I think the ANBU guys wear masks only when they go out on missions, but who knows...