Salt free and low maintenance water softener
The only thing that comes to mind for a practical "salt-free-softener" is a Reverse Osmosis (RO) system. You could also distill the entire water supply, but it's not practical unless you happen to be sitting on a lot of excess power/heat.

An RO system is rather costly and wastes a considerable quantity of water, so they are more commonly used for drinking &amp; cooking water rather than for the whole house. The principle of operation is that the water is forced through a membrane that does not allow dissolved minerals to pass through it, but a significant amount of water has to be diverted to carry that material off. 

I don't think they normally are set up this way, but it's always seemed to me that the waste-water from the process could be collected and used for toilet-flushing, irrigation or the like.

Depending on the age and condition of your salt-based softener, and the hardness of your water, you might find that you can reduce salt use considerably with a more modern unit - many older units simply recycle on a time switch, while newer ones actually pay attention to the amount of water used.