Yes. Several factors can cause the tips of your curly parsley to turn white. Most likely, this issue stems from the parsley's growing environment. Overexposure to the sun can damage plant cells and turn the tips white. Too much wind can also harm the parsley plant, stressing it out and causing the tips to turn white or yellow.  If the parsley plant goes through a drought period, that can also cause the leaves to change color. Most parsley growers have watering systems to compensate for the lack of rain, so something else likely caused it. No matter the cause, the white or yellow tips are safe to eat.