Filtered water is fine if distilled is distasteful, but you could easily find that ANY water may not be very palatable.
I tried all kinds of water on my own two prolonged fasts and found little if any difference between them, in that they were all distasteful.
In my view it is the bad taste in the mouth, experienced by many, which gives this false impression/taste.
SHELTON.............
"A frequent development while fasting is a dislike for water. This is particularly true if the water is "hard." "Hard water" that, while one is eating, tastes pleasant enough, is rejected by the sharpened sense of taste. In such cases we find the use of distilled water, to be satisfactory". http://www.soilandhealth.org/02/0201hyglibcat/020127shelton.III/020127.ch29.htm
I would personally never use anything but distilled as this is the purest/cleanest of all H2O.