Generally speaking it seems that hard water is alkaline, while soft water is acidic. Is it possible to have the opposite (hard/acidic or soft/alkaline), or is there an intrinsic relationship here such that if your water is acidic, you can pretty much assume its soft?
Hard water is usually alkaline and soft water acidic because of the minerals naturally surrounding waterways.
In nature, some mineral compounds (rocks) are Anhydrite CaSO4 and Epsomite MgSO4 that will make water hard while being acidic. Because these sulfate species dissolve easier than carbonate species they are usually less common. Mostly, we have Calcite CaCO3 and Magnesite MgCO3 which create hard water and high alkalinity.
This means, that RO water can be modified in either way;
Hard (high GH) and alkaline (high KH, high pH) using CaCO3 and MgCO3 slowly, or CaSO4, MgSO4 and NaHCO3 faster due to solubility speed.
Hard (high GH) and acidic (low KH, low pH) using CaSO4 and MgSO4.
Soft (low GH) and alkaline (high KH, high pH) using NaHCO3.
Soft (low GH) and acidic (low KH, low pH) using pure RO.