Does mixing two different foaming soap make it ineffective?
The soap solutions were originally transparent. An interesting experiment, if you still have some of the original soaps, is to shine a light thru the solutions and look for a Tyndall effect:

The light source is on the far right, out of the picture. The beaker on the right shows light scattering from particles comparable in size to the wavelength of light due to the Tyndall effect; the beaker on the left shows no scattering, even tho the light beam is passing thru it. Its contents are unknown, but there seem to be no particles of sufficiently different index of refraction and size to scatter light.
The tiny particles which scatter the light (just like in a smoky room) are micelles, aggregates of several hundred or thousand soap molecules. In the original soap solutions, this scattering is small, due to selection of manufacturing conditions (exact formulation, concentration, pH, other ingredients, etc., etc.), so the solutions appear transparent. What is optimal for each soap separately may not be optimal for the combination: perhaps the mixing produced larger micelles which scattered more, so the mixture scattered more light and became cloudy to the eye. I'm going to suggest that both soap solutions show a Tyndall effect, and the mixed solution shows a much larger Tyndall effect. It may change with time.
Now the question becomes: is the combination as effective as either solution alone. Well, it is different (cloudy). It could be worse; it could be better! It might not be observably different.
The foaming test could cast some light on the effectiveness: If you can test the foaming (height of foam and time stability) of the original solutions and of the mixture, and if they are all the same (+/- ~10-20%), the combination is probably OK.
There is a case where this foaming test will indicate immediately that the combination is not good. The molecules in soaps and detergents have a hydrophilic end and a hydrophobic end. Soaps are salts of fatty acids, and have a negative (hydrophilic) carboxyl group at one end and a (hydrophobic) hydrocarbon at the other end, and a soluble alkali metal cation. There are nonionic detergents which have no charge; they are compatible with anionic or cationic soaps and detergents. Cationic detergents (usually amine salts) have a hydrophilic positively charged nitrogen at one end and a hydrophobic hydrocarbon at the other, and some anion, usually chloride. If you should mix solutions of a cationic detergent with an anionic soap, the positive and negative charges associate to produce a neutralized ion-pair with two hydrophobic hydrocarbon groups - together this looks like a big fatty molecule with a little polarity in the middle. Overall, this molecule is not very soluble in water and precipitates out (but it floats like scum). And since it is not soluble in water, it won't foam.