There is a widespread concern that the pH swings from CO2 injection may hurt livestock.
The main reason why pH stability is important in planted aquariums is that pH levels normally reflect alkalinity (KH levels/carbonate hardness) which affects fish/livestock osmoregulation. Sensitive shrimp for example, are affected by sudden changes in carbonate salt concentrations in water and dislike KH swings of more than 3 degrees in a short time span. (This would be also reflected in the pH changing rapidly in a short time).
However, if pH is changed without a change in KH, as in the case of CO2 injection, the swings in pH do not impact livestock.
Excessive levels of CO2, and extreme levels of pH ( where the acidity itself becomes an issue ) will still affect livestock, but these are separate issues from pH swings caused by CO2 per se.
If we do large 60-80% water changes in our CO2 injected planted tanks, the pH changes a full 1.0 unit in 20-30 minutes or less, yet we never lose sensitive shrimp or fish if the other parameters are kept consistent. pH swings ( 1 full point + ) also occur in nature very commonly, as CO2 levels build up overnight due to decomposition, but are quickly depleted during light hours. Fish from acid peat swamps will do alright in a tank where the pH drops from 7 to 5.8 during CO2 injection as the low point in the cycle pH(5.8) is within range of their natural living conditions. However, alkaline water fishes may not take the dip into the pH 5.8 range well. It is not the swing, but the pH value itself being outside of the fish's natural range. The same alkaline water fish can survive a comparative pH swing from 8.5 to 7. It is important to differentiate the impact of a pH change vs the impact of an extreme pH value in itself.
Head here to learn more about important water parameters for livestock.