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No a person with diabetes should not use Epsom salts (unless your doctor says it is okay.) Epsom salts contain a high percentage of Magnesium Sulfate, which, is absorbed through the skin.
The use of Epsom salts for diabetics can cause dry skin and since dry skin is already, a frequent problem for people with diabetes it is not usually recommended.
In addition the use of Epsom salts has been documented to cause fluctuations in glucose levels again this not something a person with diabetes needs.
It is always best to ask your doctor he/she may allow a small amount of Epsom salt use for certain conditions depending on the type of diabetes you have and how well it is controlled.