Like Potassium Sulfate (made by reacting Muriate of Potash with sulfuric acid) Muriate of Potash, or Potassium Chloride, is not an acceptable organic fertilizer because of the harm it does to your Soil Food Web and is therefore not an acceptable organic product.
langbeinite, Potassium Magnesium Sulfate, or K-Mag is also a very soluble "fertilizer" knwon to be harmful to your Soil Food Web and is therefore not and acceptable organic product.
Wood ash would be an acceptable source of both Potash and Calcium except the process of obtaining that ash produces prodigious quantities of air pollution.
Composted chicken litter would be a good source, as would any animal manure if it is composted before adding to soil. There is some concern that the manure from egg factories will be loaded with antibiotics that are fed to the caged chickens in an effort to keep them laying eggs as long as possible.
Your best bet for correcting any soil nutrient deficiency is compost and organic matter. I have seen my soil go from on deficient in Phosphorus, Potash, Calcium, and Magnesium, and a soil pH of 5.7, to a soil with optimal levels of P, K, Ca, and Mg and a soil pH of 7.2 using only compost and organic matter. It did take time, 3 or 4 years, but I did not spend any of my money on "fertilizers.

I looked at the OMRI website and they still list Langbeinite as ALLOWED. I think some manufacturers add products like you describe to Langbeinite and these would not be allowed in the organic program. However, K-mag and Sulfate of Potash Magnesia do not have these added to them.

I would not recommend them though as a primary supply of potassium. They do have some salt content, although much smaller than synthetic fertilizer, and are soluble (although OMRI website lists them as having "low solubility"). I would use K-mag as a supplement to help achieve your overall K requirements.

Keep in mind that many things on the Organic Materials Review Institute list of "approved" products are there because of compromises and may not be truely acceptable to many organic gardeners/farmers.

I hear what your sayin kimmsr. I think K-Mag (although taken almost directly from the ground) is one of those "borderline" products that if you DO use it, do so in limited amounts.

On the potassium subject, does anyone know the potassium content of DRY molasses? I've read that liquid molasses is supposed to have a 1-0-5 NPK value, but have never seen anything for DRY molasses. I guess DRY molasses would serve as a good fertilizer for potassium. Would appreciate any data someone could provide.