Yes it should be safe. Fill a glass with this milky water and if it clears from the bottom up it is fine. This will be bubbles.
Hot water has less ability to hold dissolved gases than cold water. so once the water leaves the pressurised water system gases escape, in the same way CO2 in lemonade stays dissolved until you open the bottle.
This milky whiteness is basically air dissolved in the water escaping in microscopic bubbles. Any other whiteness may be chalk solutes if you are in a chalky area.