Does protection from a color prevent damage dealt by a colorless source?

Protection from a color means the protected permanent or player cannot be damaged by sources of that color, cannot be enchanted/equipped/fortified by sources of that color, cannot be blocked by creatures of that color, and cannot be targeted by spells or abilities from sources of that color (CR 702.16b). All four of these restrictions require the source to actually have the relevant color.

A colorless source — such as a colorless artifact creature, a Wastes land, or an Eldrazi with no color indicator — has no color at all (CR 105.2). Because it lacks the protected color, none of the four protection restrictions apply to it. Damage from that colorless source is dealt normally.

This is a common misconception: protection does not mean "immune to everything except the named color." It is a targeted filter that only screens out sources possessing the specified color.

Concrete example: Your opponent controls a Ulamog, the Infinite Gyre (a colorless Eldrazi). You give your creature protection from white. When Ulamog attacks and your creature blocks, Ulamog's combat damage is dealt as normal — protection from white does nothing, because Ulamog is colorless, not white.