A solid bar is not a liquid. That's the entire ruling. TSA's liquid rules, the 3oz caps, the quart bag, the tray-side triage, apply to liquids, gels, and aerosols. A shampoo bar is none of those; it goes through security like a deck of cards. Same for a conditioner bar. No size cap, no bag limit, nothing to declare, nothing to explain. As far as the checkpoint is concerned, both bars are just objects.
The bottle, meanwhile, is playing a different game: decanting into travel minis, double-bagging, and betting a bag of clothes that a cap holds at altitude. Bars can't spill. The Coconut Oat Shampoo Bar and the Cocoa Almond Conditioning Bar ride in a tin or a dry soap dish, and one bar covers a two-week trip. Your bag also gets lighter on the spot. A liquid conditioner is roughly 75% water, and until now you were the one carrying it.
The carry-on math
No liquid limits. No leaks. No 3oz cap. One tin, two bars, two weeks of washing, and the security tray never learns your name.
Two habits make it seamless. First, pack the bar dry. It lives on a draining dish at home, so give it a night out of the shower before it goes in the tin; a damp bar sealed in a tin softens, a dry one keeps. Second, mind the heat. Cocoa butter starts to soften around 85°F, so skip the parked car and the sunlit window seat. The middle of your bag is a cool, dark room.
That's the whole article, because that's the whole subject. The liquid rules were written for liquids. Switch to bars and you're no longer the kind of traveler the rules are about.