Yes, white rainbows are real!!
They occur when there is a moon in the sky. So they are called moonbows. They occur when the moon is at or below a certain angle from the horizon and the water is flowing (can either be rain or a waterfall). They are pretty rare and only last for a handful of minutes before disappearing.
Just as the sunlight comes through waterdrops, turning them into a prism to form rainbows, the moonlight comes through these natural prisms making a moonbow. These rainbows are also known as lunar rainbows.
They appear white because the amount of light reflected from the moon is less. Moonbows have the same seven colors as a regular rainbow, but our eyes cannot perceive these colors and thus they appear white.
Fun fact, the colorful moonbow can be seen in a photo taken by a polaroid camera.
They appear more frequently at locations with waterfalls that make a thick layer of mist in the air. The moonbows formed near a waterfall are usually called spray moonbows. Hope you get to see one soon.
Quite informative