Syngonanthus and Tonina species and some Eriocaulon species such as the red Eriocaulon quinquangulare (shown above) prefer very softwater.
Most "softwater" plant species are actually sensitive to high KH values and not GH per se. It is more accurate to then say that they prefer water with low carbonate hardness [low KH].
Most plants are tolerant over a wider range of GH unlike KH.
Typical softwater species such as Syngonanthus, certain Eriocaulons, can grow well in high GH (10ish) waters as long as KH is kept low; about 3dKH or less. Many aquarists may be less limited in their plant selection than they think, if they have high GH but low KH water. Between 1-2 dKH you can keep sensitive softwater species (Syngonanthus, sensitive Eriocaulons, Tonina, Ludwigia pantanal, 'Blood vomit' etc.).
Between 0-7 dKH you can keep 97% of all commercial aquatic plants in optimal condition.
8-12+ dKH you can probably grow 95% of species well, but some will be sub-optimal. Above 18 dKH or so, more issues start arising with regards to growing plants.
Syngonanthus species tend to favor very softwater and acidic substrates. (less than 3dKH). Ludwigia glandulosa (purple plant above) is much more flexible and takes medium-hard water well.
The spiky Centrolepis Drummondiana 'Blood vomit' prefers very softwater, while the purple plant above, Bucephalandra 'Brownie ghost' actually does well in hardwater. When mixing species, one must give way to softwater plants.
Rotala macrandra (mini type 4 shown here) prefers softwater water, but can tolerate well KH values up to 7dKH or so.
A number of species face stunted tips regularly when combining heavy water column fertilization (i.e. EI method) with alkaline water. This list includes many Rotala species, such as Rotala macrandra and its variants, Pogostemon erectus, and most Ammania species. The higher the KH, and the heavier the water column dosing, the greater the chance of getting stunted tips.
For the above species, they can grow well in more alkaline water tanks (5-8dKH) as long as they are being substrate fed with lean water column dosing (i.e. NO3 levels <5ppm).
My Seiryu rock scape below has a KH of around 7 to 8. Rotala macrandra (mini type 4) and Pogostemon erectus grow well with rich substrate, lean water column dosing.
Unfortunately, it is much harder to remove dissolved minerals from water than it is to add them in. You can get hardwater from adding limestone, Coral chips, or Carbonate salts (K2CO3 for example) to the tank.
To soften water, you need to remove the carbonate ions. The main way to do this is by using an RO (reverse osmosis) filter, which removes all GH/KH by filtering through an ultra-fine membrane. RO water needs to be remineralized before use.
RO filters are a common tool for aquarists seeking complete control over their water parameters. It extracts out all salts/impurities, and give a blank slate for hobbyists to add their own additives.
The alternative method is to apply a strong acid such as Hydrochloric acid (HCL) to water before adding it to the tank - it breaks down the carbonates in water into CO2. (but this method carries its own risks)
Peat and aquasoils will reduce KH and soften the tank water as well, but this only lasts as long as the buffering capacity last. This may work for tanks at the borderline - for example if your tap water is KH 4, and you want to grow Toninas, using Aquasoils will drop the KH to near 0. Depending on peat/aquasoils to drop the KH from very alkaline water will deplete their buffering capacity more quickly. These resin will have to be renewed as their buffering capacity get exhausted.
For detailed care guide to the aquarium plants above, click here.