Distillation produces water with essentially nothing in it, including no organisms, and that is the point at which most discussions stop. But water with nothing dissolved in it has no disinfectant residual and no buffering, which makes what happens between the condenser and the glass more consequential than it would be for tap water.
Why storage matters more here
Municipal tap water carries a chlorine or chloramine residual that continues suppressing growth in a container for a while. Distilled water carries nothing. So a jug of distilled water left open on a worktop is colonized from the air and from hands considerably faster than the same jug of tap water, and there is nothing in it working against that. Sterile at the point of production is not the same as sterile at the point of drinking, and the gap between the two is entirely down to handling.
Containers and what they contribute
Because it is aggressive and unbuffered, distilled water takes up whatever a container offers more readily than mineral water does. Use food grade containers intended for water, keep them clean and capped, and avoid storing it long term in metal, which it can corrode. It also absorbs carbon dioxide from the air on standing, becoming slightly acidic and picking up a faint sharpness, which is harmless but noticeable and is one reason freshly produced distilled water tastes different from a bottle that has been open a week.
Practical handling rules
Keep it capped rather than in an open jug. Refrigerate what will be drunk over the next day or two and treat it like any other prepared food. Do not top up a partly used container with fresh water, since that keeps whatever colonized the old batch in circulation, and wash and dry the container between fills. Clean the still's boiling chamber regularly, because the residue left behind concentrates everything the water contained and is exactly what you were removing.
The other half of the answer
Once storage is handled, distilled water is a perfectly safe daily drink for anyone eating a normal diet, and the remaining objections are taste and the small mineral contribution it does not make. The USGS classes water as soft at 0 to 60 mg/L as calcium carbonate through to very hard above 180 mg/L, so what is forgone depends on the supply it replaced. A remineralizing stage answers both at once. Our drinking water guide covers the options.
Questions people ask about drink distilled water safe
Is distilled water sterile when I drink it?
At production, yes. After that it depends entirely on the container and handling, since it carries no disinfectant residual.
What should I store it in?
Food grade containers intended for water, kept clean and capped. Avoid long term storage in metal, which it can corrode.
Can I top up a partly used bottle?
Better not to. Topping up keeps whatever colonized the old batch in circulation. Wash and dry the container between fills.
Why does stored distilled water taste sharper?
It absorbs carbon dioxide from the air on standing, which makes it slightly acidic. Harmless, but noticeable against fresh water.