I think that in this case, hair braids are a Tau thing, not just limited to the Fire Cast.
Possibly, though as we are dealing with four distinct ethnic groups, it seems likely that each caste would have its own traditions. I agree with you that the Fire caste, and the Air caste too for that matter, would be among the most traditional, owing to their greater isolation from Tau society as a whole, but all castes likely have distinct customs.
Then, naturally, different septs and worlds will have their own ways, and even different groups within those groupings according to social links across caste lines, and so on and so forth. As such I wouldn't generalise that all Tau will braid their hair (just as, in your analogy, not all humans are tattooed or pierced). It may be traditional, evoking images of honour, respectability, the martial pride of the ancestors, etc., but I'm sure their sense of style goes beyond just that.