He doesn't like how it makes Schala an accessory to the arrogant policies of the Zeal Court and royal family. Yet, I think he seems to forget, Schala has complicity, or at least not enough strength and moral fortitude, to openly disobey her mother. She could have refused to activate the Mammon Machine, and Lavos would not have been summoned. Her weakness in not disobeying the Queen her mother doomed her land, for she only needed refuse: her life for her people. But for whatever reason, she did not. This either makes her coward, or not fully against the aims and goals of the family - following her mother's lead while still bearing sympathy for her victims. She was not that old, after all, and was just a young girl caught amidst a very trying time, and likely found it very difficult to choose sides, or right and wrong.
Now, the fact of the matter is, ancient people could well have had dye. Dye is obtained from seashells, or ground rocks, or any number of other places that are easy to find. Some, like Purple, were far more valuable, but dye is still an extremely ancient invention. For a kindom that has flying machines advanced beyond that even of Crono's time, dye is not a great leap.
Now, personally, I prefer the dye solution immensely, for two reasons. Firstly, such adornment as a status symbol is quite interesting: sort of like the way the pharaohs of Egypt always wore their beards in that certain way, and wore the double crown, and bore the crook and flail as symbols of leadership and the like. For the royalty of old Zeal to mark themselves in a certain manner is simply following the mould of ancient societies. The second reason is simply this: multi-coloured hair is just over-wrought and silly, and cannot be taken seriously, which I prefer to do so far as Zeal is concerned. I mean, to you really think that Zeal was only so big as it shows? Surely there were far more people, else it was smaller even than the first walled-cities of mankind, smaller than ancient Jericho and Catal Huyuk. Each of those had in the thousands, even tens of thousands. Zeal by its level of advancement must at least have the numbers of Uruk or Babylon. How did they supress all other peoples? Surely, they have magic, but if magic is unique to them, it is likely that the numbers arrayed against them were far more, and even great power can not victor against overwhelming numbers. So I'd figure they had a mighty army. None of this is shown, and might be thrown in with the whole thing of hair-dying, but it gives a serious light to Zeal, making it more of an ancient and hallowed things of ancientry.