For what it's worth:
My household has been using for the last four months a three-stage filter system that includes a coarse particulate filter, an activated-charcoal filter, and a greensand iron/manganese filter.
This filter system is not advertised as reducing water hardness, but in our experience it does. Testing by our local lab shows that unfiltered, our water has a hardness (CaCO3) of around 70 mg/l. Filtered, the hardness is essentially eliminated (the test comes back as "not detected").
The downside? These filters are lasting a fraction of their advertised lifetime for us. The manufacturer tells us that the filters should work for 90,000 gallons, given our water condition (around 100 mg/l TDS, which apparently is the biggest thing they worry about in terms of effect on the filter, other than the substances actually being filtered). But in practice, we are seeing the efficacy of the filters reduced quickly under use, requiring replacement after around 9,000 gallons. I.e. they last only a tenth of the time they are advertised to.
The manufacturer has told us that they don't expect for the water hardness to be a problem, but they also say that the filters shouldn't be removing hardness from the water. My interpretation of our experience is that they are mistaken on both fronts, leading to the CaCO3 getting caught by the Fe/Mn filter, causing it to be saturated much more quickly than expected.
For us, the cost of the filter is high enough that we are looking into alternatives (but we're hoping to find a salt-free option). But depending on one's goals and existing hardness levels, it might be worth a try. The initial install cost was very low (the filter housing and three filters included is only about US$500). A salt-based system will be much less expensive, but our experience shows that it is possible to remove hardness without salt, albeit at increased expense (and since the bulk of the expense is the filter cartridge, an on-going expense, it will eventually exceed the cost of most other options, including reverse-osmosis).