The short answer
Salt-free media is sensitive to iron, manganese and sulfur; makers set low limits, so well water often needs filtration first.
The limits
Makers list maximum hardness and low limits for iron and manganese; check the listing against your test.
Options
TAC conditioners: AQUIOS TS220S Salt-Free Conditioner and Filter System, Kind Water Systems E-3000 Salt-Free Water Conditioner. Iron filters for wells: iSpring WCFM400K Air-Injection Iron Filter.
When salt-based is better
For very hard water or water with iron, an ion-exchange softener (with an iron filter ahead of it) is the more reliable fix.
Products mentioned
Conditioner and filter combo · AQUIOS
AQUIOS TS220S Salt-Free Conditioner and Filter System
Conditioner and filter combo · 15 GPM
Salt-free TAC conditioner · Kind Water Systems
Kind Water Systems E-3000 Salt-Free Water Conditioner
Salt-free TAC conditioner · 15 GPM
Air-injection iron filter · iSpring
iSpring WCFM400K Air-Injection Iron Filter
Air-injection iron filter · 12 GPM
Questions readers ask
Can I use a salt-free softener on well water?
Only if iron, manganese and sulfur are within the maker's limits.
Do salt-free softeners remove iron?
No; treat iron separately.