Inquiry
Why did Schala's hair turn blonde in Chrono Cross? Note that her eye color also changed from green to blue, leaving this as a possible plot inconsistency.
Theories
Schala Hair Dye
While the royal family of Zeal all had naturally blue hair, Schala did not. Instead of allowing her to be ridiculed, the royal family of Zeal simply had her hair dyed blue to match the others. This dye wore off during her internment inside the Time Devourer.
Bleach Effect / Genetic Alteration
Chrono'99
The nature of the environment of the Darkness Beyond Time and the Time Devourer caused her hair to become chemically bleached. However, this would mean her scalp would suffer from the same effects, which is problematic. Also, why would Kid have blonde hair?
Another tenet of this theory holds that since Lavos was able to recombine DNA, the Time Devourer made some changes to Schala when she unified with it. This might have changed her hair blonde and her eyes blue, which means any copy of her (Kid or Harle) would keep the effects.
Misconceptions
Comprehensive Hair Dye
The people of Zeal did not simply dye their hair blue, or Janus would have lost his hair color as well after training with the Mystics. One may object that he dyed his hair even in 600 A.D., but even his Chrono Cross shell (Guile) has hair intended to be naturally blue and purple.
Magic Drain
This theory contends that the hair of the people of Zeal appears blue when they are charged with magic power. It holds that when magical power is lost, the hair turns back to blonde. Why, then, did Magus's hair not turn blonde after he summoned Lavos and later challenged the beast in the Ocean Palace? Why didn't Schala's after the entire ordeal lapsed and she only had enough power left to transport the party out? What about Queen Zeal? One can argue that these instances were neglected because the developers did not want to make blonde sprites and palettes. Even at this stage, however, it is a stretch.