Well, I guess they’re consistent. Sort of.

It seems that some people are concerned about our new habit of wearing cowboy hats during academic ceremonies at Southwestern Baptist Theological Seminary. The complaint is that wearing a cowboy hat is somehow undignified and inappropriate.
Please realize that the mortarboard that most modern academics wear as a hat actually derives from the medieval Roman Catholic priesthood. You see, in the Middle Ages, every university student was also a cleric, in the lower orders of the Roman priesthood. The biretta/mortarboard identified one as part of the lower Roman clergy, and the birettas became more colorful as one rose higher in ecclesiastical rank (for instance, purple for bishops, scarlet for cardinals).

Please realize that the long colorful cowls that we wear over our robes are actually hats, too. Yes, the cowl and the robe with the long sleeves were originally part of a monk’s habit. You see, in the Middle Ages, not only was every university student a cleric, but most were simultaneously under monastic vows. The cowl was used to cover one’s head in the cold and damp weather in Europe, and the long sleeves were handy for carrying such things as writing paraphernalia and one’s lunch.
Now, honestly, what is more relevant and dignified in a Texas free church setting: A cowboy’s hat, reflecting our ministry to and identification with our people? Or, a priest’s biretta, indicating we are ontologically superior to our people? Is it not part of our Baptist Reformation heritage to alter mere trappings as we see fit? We are neither in Roman orders nor under Roman custom. We are Southern Baptists, and as free churchmen, we are free to reform our customs and habits as we deem fit.
We are Southern Baptists in Modern Texas, not Roman Catholics in Medieval Europe, and we will wear common cowboy hats rather than exalted sacerdotal birettas, in honor of our great free churches and in order to identify with our great people. (Via Bill MacKinnon at BHT.)

Well, no one says that goofy academic regalia is an inalterable aspect of reality. And this is consistent, as I say, with some historical rejections of things like Christmas among some Protestant traditions. But you know, I hear that “Gregorian” calendar was thought up by some papist. Hey! I think it was a pope!
A Baptist pastor/blogger critiques the decision and reasoning here.