Very believable. Quite frankly they could contrive whatever reason they want to justify radically different uniforms. At least for the people who care that they're radically different.Am I the only one who thinks a new uniform design would actually be more believable in context with canon? Canonically the TOS-movie era uniforms were in use for the longest period of time (at least up until 20ish years before TNG based on Deanna's dad wearing one) and they were completely different. It seems the rainbow jumpsuit style was only used for the decade or so around TOS, then fell out of favor for a century until it was revived in the TNG era which again only lasted for a few decades before it reverted back to a predominately-single-color two-piece uniform again. It's just not a popular design.
Plus, we know that each ship was already using individual badges in the ENT to TOS era. It would not be much of a stretch to retcon that the whole TOS-style itself was limited to certain ships or classes of ship.