If it helps you feel any better, Disneyland tap water is also super gross. Los Angeles is a barren wasteland of a place with no water of its own - any water Orange County gets is brought in from elsewhere, and it all ends up gross at the end of the day. Granted, I'm spoiled in the Bay Area by delicious Hetch Hetchy water, so I'm a little biased.
Honestly, water's the one thing I'm dreading in my upcoming week-long WDW trip. I take a medication that leaves me at greater risk of dehydration so I need to be drinking a ton of water throughout the day, especially when I'm particularly active. I've already got packets of Gatorade here so that I've got a quick way to boost my hydration and make Florida water taste like something, but I'm honestly considering just going the "grab a case of water at Publix" route. The rooms have open fridges, might as well use it.