You're mixing up a lot of different things together.
As the previous post explained, sulphites and sulphates are very different.
Epsom Salt is magnesium bonded to sulphate. Sulphates are just oxidized sulphur, or sulphur with oxygen attached.
Some people are sensitive to sulphur, but this can also be a detox reaction since sulphur is very reactive. So you have to differentiate between a sulphur reaction, magnesium reaction, and a detoxification reaction.
As far as the moritz Liver Flushes go, there is a whole lot more to the flush than just the epsom salt. If you want to test for a reaction to Epsom Salt then just take Epsom Salt without doing a liver flush.
Sulphur reactions (*not sulphite reactions*) are very common in people with heavy metal toxicity, not because of the sulphur but because of its reactivity with the metal. So really what they are seeing is an induced heavy metal reaction and not a sulphur sensitivity per se.
Sulphur is known as the skin mineral. If you have dry skin or are prone to rashes or any other chronic skin problem it is likely you are deficient in sulphur.