This is a bit of a loaded question. Technically the answer is no, but if you don’t use salt you have to use something similar. Much like grocery stores sell shakers of salt-substitute for people on a sodium restricted diets, some stores that sell softener salt also sell a water softener salt substitute called potassium chloride. The potassium chloride for softeners is just as effective as regular softener salt but adds potassium instead of sodium.
The cost of potassium chloride is higher than regular softener salt and it can be harder to find in stores but may be well worth compromises if you have concerns about residual sodium in your water. Call and check on the availability of potassium chloride and the difference in price, compared to softener salt, in your area.