ACUTE effects of drinking distilled water
The idea behind the myth that distilled water is harmful is that its low osmolality ("tonicity") could dangerously decrease the blood osmolality, which is normally: 285-295 mmol/kg. But distilled water has only slightly lower osmolality (0 mmol/kg) than tap water (~3 mmol/kg) (SGSM.ch, Table 2), so if drinking appropriate amounts of tap water does not significantly lower blood osmolality, distilled water also shouldn't.
What happens when you drink distilled water:
- It is mixed with gastric acid and fluids in the intestine, so at the time of absorption, it's no longer distilled water. Also, at a certain time before and after drinking distilled water, you probably eat something and thus likely get more minerals with food than with most types of water.
- When absorbed, it tends to lower the blood osmolality, which is sensed by osmoreceptors in the hypothalamus, which signal the pituitary gland to decrease the secretion of the antidiuretic hormone, which stimulates water excretion in the kidneys until the blood osmolality is corrected (Colostate.edu).
You can find "distilled," "demineralized," "reverse osmosis" and "purified" bottled waters in grocery stores on the shelves together with other beverages, so they are not likely "dangerous."
CHRONIC effects of drinking distilled water
The idea behind the hypothesis that long-term intake of distilled water could be harmful is that it could leach minerals from your body. A 1980 report by World Health Organization says:
Salts are leached from the body under the influence of drinking water
with a low TDS. (TDS = total dissolved solids)
The 1980 WHO report has been criticized in a 1993 report by Water Quality Association who have found no reliable evidence about harmful effects of water with a low TDS on health:
It has been concluded that the consumption of low TDS water, naturally
occurring or received from a treatment process, does not result in
harmful effects to the human body.
Another argument against distilled water is that it doesn't contain "healthy" minerals, such as calcium and magnesium. But a list of tap waters from 100 US cities shows that average tap water contains less than 50 mg Ca and less than 10 mg Mg per liter. So, by drinking 2 liters of tap water per day you could expect to get less than 100 mg Ca and less than 20 mg Mg, which contributes only little to the Recommended Dietary Allowance for adults (Ca = 800-1,000 mg/day; Mg = 350 mg/day).
About water intoxication
Any water, distilled or tap, and other beverages that are low in sodium can cause water intoxication (dilutional hyponatremia) if you drink them a lot in a short time, for example, more than 1.5 liters per hour for several hours in a row (Research Gate), because your kidneys may not be able to excrete more than 1 liter of water per hour. Again, distilled water is not significantly worse than tap water in this regard.
In conclusion:
Distilled water is not acutely dangerous and there is no reliable evidence of its eventual chronic harms. Anyway, demineralized/distilled water may not be the optimal beverage because it has a flat taste and does not contribute to calcium and magnesium intake.