Short answer: Yes, almost always. That cloudy water from air bubbles is 100% safe. It’s just water and air. Your body is mostly made of water and air, so you’re fine.
Why Is Tap Water Sometimes Cloudy And Is It Safe To Drink
Even the sediment is usually just harmless grit. It might taste like a sidewalk after a rainstorm. But it won’t hurt you.
The only time to worry is if the water smells like bleach, rotten eggs, or metal. That’s a different story. Call your water company. They love explaining weird smells. It’s their job.