Is tap water in asia safe to drink or should I throw it away?

Depends. Water quality runs the whole spectrum from safe to lethal depending upon where you travel. Remember that people from the region you are in may be accommodated to the "bugs" in the water supply, and as an american you may react with GI disturbances to the very same water. I remember being warned to drink and brush my teeth with bottled water in mexico when i was young (this was the 1950's)!
In general. recommend against drinking tap water in Asia. This comes from having lived in Asia three times. I would not trust any water that is not poured from a sealed bottle before you eyes.
Depends. Asia is a huge area. Singapore has incredibly clean water, laos not so much.Drink water from safer sources than the tap.Expect some GI changes when traveling as common U.S. Bugs are what your body knows;others may cause minor(or not) problems.