it is unlikely to be dangerous, plain tap water is not that conductive, almost not conductive i've heard of people doing immersion cooling with computer hardware using distilled water on the other hand, the water out of the tap is conductive enough to earth you for the typical levels of electrostatic imbalance common from being constantly isolated from the ground

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also, most mains water is already buried in the ground and amply earthed, so even if pipes exposed to the air were struct they would discharge right there not conduct all the way to your shower and take such a high resistance path to earth