Most fish/shrimp are not sensitive to fertilizers in the normal dosages that is required for plant growth. Most fertilizers comprise of common elements available in natural waters. Commercial brands do not introduce them in high enough concentrations to affect livestock. For commercial brands, the recommended dosage rates generally have so wide a safety range that even a 10 times overdose does not harm livestock. In controlled drop tests I conducted on neocaridina shrimp, a 10X overdose of common fertilizers like Seachem Flourish comprehensive had no affect on the shrimp.
Some aquarists have concerns over copper in fertilizers; however, commercial fertilizers for aquatic plants only contain copper in minute amounts - far too minute to be harmful.
The exception to this scenario are folks that DIY their own fertilizer mixes by using fertilizers calibrated for terrestrial plants. Over-loading greatly with heavy metals found in trace element packs could impact livestock.
It is common for planted tanks to keep shrimp. They consume detritus and breakdown organic waste and are a useful addition to any planted tank.
However, livestock can be sensitive to high CO2 levels and instabilities such as rapid changes of water parameterscaused by large water changes when the tap water is different from tank parameters.
High CO2 rates can affect brood rates for CRS shrimp. Large flux due to water changes can cause excessive moulting. Neocaridinas are much more tolerant.
This is marketed as a 'Carbon supplement' and is not strictly considered a 'fertilizer'. However, it is significantly toxic and will kill livestock if overdosed. Folks breeding sensitive shrimp should avoid it totally. Its marketed effect as a Carbon source for plants is of questionable efficacy at best, so I would advise against its usage in any tank for that purpose.
It is useful as an algicide, but should be spot dosed to maximize its efficacy.
When doing water changes, check that the key water parameters are similar: TDS, GH, KH, temperature.
For recommendations on water parameters test kit, please see link here.