It's the opposite, actually. It might not be that you dislike the taste of microwaved water, it might instead be that you have become accustomed to the taste of water that has gone through your other method, the same way you might (as an example) learn to prefer fridge water stored in an iron pot (thereby giving the fridge water more of an iron-y taste).
Similarly, you might just be disliking the taste of microwaved water because there's something in your microwave imparting a taste to water which is microwaved there, the same way that your butter can start to take on the taste of onions if you leave uncovered onions in your fridge.
EDIT: If you do decide to do the Pyrex dish experiment, be careful handling the microwaved water
just in case it is superheated.
--Patrick