Distilled water is perfectly safe to drink. People (most likely NOT from a science/biology background) argue that distilled water is so pure that it will pull out all your electrolytes due to the "desire" for the two substances (the water, and everything in your body) to equalize.
The difference between tap water and distilled water isn't that profound in most areas, the dissolved minerals in the water are miniscule and compared to what is in your body already there might as well not be any. It most likely wont leach calcium from your bones (a common myth), because the amount of calcium in your blood contains somewhere around +10x the levels of calcium of tap water. Blood (normally) contains >100mg/l of calcium while tap water normally contains 1-100 mg/l. By this logic most people's tap water would be "robbing" them of calcium and other nutrients.
If anything, too much calcium (and other minerals) in drinking water can be more of a health concern especially to those who are prone to kidney stones.
tl;dr as long as you aren't chugging like 5 gallons of distilled water a day without any meals, you will be fine.