We had a reverse osmosis filter fitted for the same reason as you 8 years ago. Get it serviced every year and have had no issues from it. Use it for all our drinking water. I wouldn't like to drink the water that comes through the softener without it going through the filter first.
Not sure about Leo's comment but our water, if untreated, would contain high amounts of iron and manganese and this is why we have our kitchen tap fed from the softener. If lime in the water is your only problem it would be fine to drink but you need to bear in mind other minerals that could be present.