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If your shea butter smells rancid, don't use it. It normally smells kind of nutty. Before making anything with it, you can heat all of it to 160ºF, stir it very well, and then quickly refrigerate it to cool off. That should give you a smoother consistency for making other soap and other products.
As for your soap, if those white spots feel like soap or wax, they are mostly likely stearic spots, not a result of bad shea butter. Stearic spots are cosmetic only, not dangerous.
To prevent them, be sure heat all of your solid oils and butters to at least 160ºF. Then mix those melted hard oils very well with the other liquid oils before cooling them down and adding the lye solution. That ensures that all of the stearic acid is fully melted and incorporated with the other fatty acids, and prevents the spots from developing.
However, if those spots feel crusty or crunchy, that could be unincorporated lye crystals, which would be quite dangerous. It doesn't look like that from the pictures, but please check to be sure.
As for your soap, if those white spots feel like soap or wax, they are mostly likely stearic spots, not a result of bad shea butter. Stearic spots are cosmetic only, not dangerous.
To prevent them, be sure heat all of your solid oils and butters to at least 160ºF. Then mix those melted hard oils very well with the other liquid oils before cooling them down and adding the lye solution. That ensures that all of the stearic acid is fully melted and incorporated with the other fatty acids, and prevents the spots from developing.
However, if those spots feel crusty or crunchy, that could be unincorporated lye crystals, which would be quite dangerous. It doesn't look like that from the pictures, but please check to be sure.
