Iodized salt (table salt aka sodium chloride with iodine added) is fine in this type of soap. The amount of iodine in the salt isn't enough to cause problems. People don't use it when canning food, because sometimes the iodine can darken some foods. But I've used iodized salt interchangeably with canning salt (fine-grain plain sodium chloride) for soap making.
Dead sea salt, on the other hand, contains large amounts of various minerals. Some of these minerals will react with soap to form insoluble, sticky soap scum. Other minerals can make the soap permanently soft. So I'd avoid dead sea salt for soap making.
Same goes for any other "salt" that isn't sodium chloride (table salt). For example, epsom salts (magnesium sulfate) is another salt that people sometimes put in soap, to their regret.
Dead sea salt, on the other hand, contains large amounts of various minerals. Some of these minerals will react with soap to form insoluble, sticky soap scum. Other minerals can make the soap permanently soft. So I'd avoid dead sea salt for soap making.
Same goes for any other "salt" that isn't sodium chloride (table salt). For example, epsom salts (magnesium sulfate) is another salt that people sometimes put in soap, to their regret.