Walt Disney World distributes identical, featureless water bottles in black pouches to all of its operations and custodial CMs (to my knowledge). It's usually attached by a clip to their back hip. Obviously CMs aren't supposed to be sipping from it while checking seatbelt buckles or anything like that, but there are positions like outdoor greeters (which involve talking with guests for hours under the hot sun) where water is absolutely necessary. These were implemented years ago after health/safety concerns.
Having the water bottle filled with anything but water, or being seen buying or drinking from a restaurant cup onstage, would definitely get a CM in trouble at WDW.
They should do this at Disneyland. Being outside in the sun or talking all day, in particular, require a lot of hydration. Having an approved water container onstage is probably a lot more efficient than having CMs walk backstage over and over again to get water. And people did drink in the old West, in Victorian times, etc. It's really OK.
Was the Mansion hostess actively drinking from the Styrofoam cup as she walked by you? Or was she just holding it in her hand? You aren't allowed to drink while Onstage, but you can certainly carry a cup of water from one place to another.
That's what I would wonder too, if she was just transporting it. She could have been getting water for a sick guest or colleague, for instance. When I was in a customer service job there were several times I had to go get water (and in one case, orange juice for a crashing diabetic) for people who were sick and couldn't move, and the only way to get it to them was to carry it over.
I don't see any issue with a Haunted Mansion CM walking about New Orleans Square. Is the Mansion not a recreation of a Greek revival style plantation Mansion seen all over the south? I would have an issue if this CM was grabbing a slice of pizza from the Pizza Port in Tomorrowland. I think it's OK if a CM is still in their assigned themed land, so this is not a real big theme breaker to me really. I believe if you spend more time looking for faults than you do enjoying yourself, the magic has been lost to you anyways. It's Disneyland, have fun! It's not like you are out in front of the Haunted Mansion and there is a giant Alligator playing a trumpet or something right? Oh wait a minute....