Chemistry of stuff doesn’t depend on just acidity and basicity. When you’re dealing with things like HCl and NaOH then they ‘cancel out’ since you’re left with H2O and NaCl at the end, but the salt isn’t necessarily harmless.
A common soap product is sodium laureth sulfate, which is already a salt (hence the sodium); it’s produced as sulfate-containing compound (-SO3H), an acid that is then neutralized. So by the time you’re encountering it, it’s already in a salt form.
TL;DR: salts aren’t guaranteed to be safe. The salt-form compound can still be harmful to you. Even though the acidic or basic part of a molecule is neutralized, the rest of the molecule can still have effects.
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