Yes, mollies can live in tap water. Mollies are very hardy and can tolerate various living conditions quite easily.
With that said, you need to beware of water contaminants. Tap water in certain areas may be contaminated with heavy metals or chemicals that can harm your fish.
Additionally, mollies cannot live in soft water. Molly fish require hard water to thrive, so you should check your tap water’s hardness before adding any to your tank. If your tap water is soft, you should add crushed corals to the tank’s substrate to increase the hardness.
Lastly, you should check the water’s pH. Mollies require a pH of 7.5 to 8.5. Again, if the pH is too low, adding some crushed corals could help.