I have white moths, or butterflies laying eggs on my Radish Plants, What are they?

Cabbage moths that will lay eggs that will eventually become cabbage loopers. yes the caterpillers will do great damage to the leaves (but not the roots)

Hand pick off all eggs and the caterpillars daily. Apply Bt (Dipel) daily either early morning or evening (best) as sunlight will break down the Bt in a few hours.

Row covers put on when planting are also very effective

Other crops effected by the moths/caterpillars are cabbage, broccoli and kale (these are all in the same family as radishes)

The eggs are going to grow and start eating the plants. It is best to get rid of them which ever way you can.