For most individuals, the amount of sodium present in softened water is not a health problem. If however, you are trying to maintain a low sodium diet, this can add to your difficulties.
The amount of sodium in softened water can vary. According to a paper by Yarows et al., (Sodium concentration from water softeners, Arch Intern Med. 1997 Jan 27;157(2):218-22) the sodium concentration of softened well water averaged 278 mg/L but the variation was very large. Levels from 46 to 1219 mg/L were observed. 17% of households had sodium levels above 400 mg/L. The amount of sodium that gets added depends on how hard the water is to start with. If the water is very hard then the sodium level will be higher, as shown in the table below.
There are types of water softeners that do not add sodium to the water. Alternatively, if the ion-exchanger type of water softener is regenerated using potassium chloride, instead of sodium chloride, then potassium would be added to the water instead of sodium as the water was softened. However, in some patients with renal or cardiac disease, diabetes or high blood pressure, there can also be complications due to increased potassium intake so this should only be performed in consultation with your physician.
Finally, drinking LESS water is NOT a solution to this problem. In order to clear sodium from the body effectively, the kidneys need water. Higher rates of urine production allow greater amounts of sodium to be cleared, which is why diuretics are commonly prescribed to Meniere's patients. Ideally, you should follow the widely recommended guideline of drinking 8 glasses of water, each of 8 oz, per day.
Buying distilled water or using reverse-osmosis purification of your water for drinking may be an option.
I would be interested in hearing from patients who have previously dealt with this problem. I'm particularly interested in whether your symptoms changed after installing or removing a water softener and whether water softeners have any imapct on the management of Meniere's disease.