The main issue for both plant/livestock is that while many can survive in a large range of GH/KH values, the transitioning process from water bodies with different salt concentrations can be stressful. It is mainly the difference in alkalinity and salt concentrations that cause osmotic stress when transferring livestock between two different water bodies. The difference in alkalinity can be measured by the water's KH value.
For example, Red Cherry Shrimp can be found thriving/reproducing in tanks with as low as 1-2 dKH as well as tanks that have much more alkaline water, at 12+ dKH.
However, if we transfer shrimp directly between these 2 tanks, we will lose a good number of them due to osmotic shock as the KH value difference between the two tanks is very large. In both tanks, the shrimps have adapted to their water parameters.
Further more in CO2 injected tanks, livestock have to be acclimatized to the CO2 levels in the tank. Getting past this is generally easy - only add livestock when CO2 injection is turned off, never add them when the tank water is CO2 saturated.
when drip acclimatisation works...
For sensitive species such as dwarf shrimp, transferring them between tanks with KH difference of 3dKH or more is stressful & potentially deadly. The symptoms of osmotic shock are often not immediate - it takes many hours/days for the stress to play out, so seeing livestock moving around the tank environment in the couple of hours after adding them to the tank is not the correct way to verify whether livestock is suffering from osmotic shock or not. Shrimp that has been hastily introduce to a tank stress and weaken over many days, not immediately. This is why many folks claim that they see the shrimp moving around fine after being introduced, but go missing by the end of the week.
One way to get around this problem is to buy livestock from dealers that have similar water parameters to your own tank - this is especially so for sensitive species such as shrimp. If the difference between tank water is small <5dKH, drip acclimatization across many hours will work to minimize stress. If the difference is very large (i.e. 10dKH+), acclimatization will take days, and there is no quick method to go around it.
You can drip acclimatize new livestock by running a thin tube (aquarium air line tubes pinched with a clip works well) from the aquarium to the bag that livestock came in. Aim to double the amount of water in the bag every 2 hours or so. You can remove some of the bag water as it fills with aquarium water. You can add the livestock to the tank after 2 to 4 hours.
Sensitive livestock such as these Sundadanio axelrodi do not like large fluctuation in water parameters.
and when it may not
Drip acclimatization does not work for large parameter differences. If the difference is large, for example, 10dKH, drip acclimatization will not be enough.
In such cases, you can place the livestock in a holding tank, and raise the parameters in a holding tank slowly, 2-3 dKH a week, until it reaches the target required parameters of the main tank. The much easier option is to buy from dealers that hold livestock breed in water similar to your tank parameters.
Plop and drop?
In many situations, livestock can be dropped straight into the tank without going through drip acclimatization. The main advantage is that sometimes livestock that has been transported for long journeys suffer from a buildup of ammonia in the bag - the benefits of introducing them immediately outweighs the potential transition stress of remaining in ammonia saturated water for a prolonged period.
Adding alkaline tank water to a bag of ammonia rich acidic bag water is potentially deadly as ammonia toxicity spikes with alkalinity - Ammonia is more toxic above pH 7.
For most commercially breed fish, they are hardy enough to withstand quite a large difference in water parameters. So removing the fish and adding them directly to the tank makes sense for many species.
I would not try this approach if the parameter difference is huge - i.e. from a 1 dKH bag to a 10 dKH tank.