The etsy bar you link to has SLS, dimethacone etc! Far from natural. But still, the pH will be too high for hair. Might as well use a natural, plant derived close to natural shampoo.
Paddington Bear: Actually, the bar I linked to, GetLathered, does NOT contain SLS; Sodium Laureth Sulfate. Sodium Laureth Sulfate (SLS) and Sodium Lauryl Sulfoacetate (SLSA) are very different things. She doesn't use SLS on purpose. The Lush bar does use SLS.
Sodium Laureth Sulfate, or Sodium Lauryl Ether Sulfate (SLES) is often avoided because it may be carcinogenic. Most store bought shampoos and many cosmetics contain it. It is an inexpensive detergent, surfactant and foaming agent. It is a mix of sulfuric acid, monododecyl ester, and sodium salt. You're right, it is not natural. (not to say that "natural" always equals healthy and "chemical" always means dangerous, but I try to avoid SLS, too).
SLSA,
Sodium Lauryl Sulfoacetate is made from coconut and palm oils; a safe surfactant (foaming agent) for both skin and hair. This mild plant derived surfactant creates lather that removes removes suface oil, dirt and bacteria, without stripping or drying sensitive skin. Sodium Lauryl Sulfoacetate also dissolves more readily in water. thus providing superior rinseablility. You shouldn't need a vinegar rinse after using it.
Another ingredient you may find is Sodium Lauryl Lactylate, which is derived from palm kernel and sugar, a safe, skin friendly cleanser for both skin and hair.
As for pH, true soaps are made with sodium hydroxide, lye. The lye is gone after saponifying the oils, but the pH of soap is too high for many people's hair, as you said. Using a vinegar rinse afterwards can counteract that to some degree, but who wants to carry vinegar with them. This is why I recommend a "syndet" shampoo bar, as made by GetLathered.
I can provide links to sites that explain this more fully if you'd like.