Is it okay to eat settler-colonists moving into your space? Flesh is not food. Eradicating a consequence of animal exploitation does not give one ground to exploit animals anyway, as a treat. Sterilization programs are effective when possible so you don't end up poisoning scavengers.
The entire question is a bit ill-posed, anyway, since most invasive species are not hunted for food (and, indeed, most of them aren't animals). The problem with invasive species is not that they exist, it's that they have no ecological limit on their proliferation and thus outcompete local species. You solve this with proactive population control, the same way you spay/neuter domesticated animals.
The incentives of hunting for "population control" are all wrong. These programs seek to control the population in order to perpetuate the practice of hunting and the "profit" of those hunts. Deer overpopulation means ecological impact and resource contention, which means starved and sickly trophies. Reintroducing the natural predators that were eradicated by humans restores the ecological limit on the population and repairs the broken nutrient cycle humans created, no murder program required. This is simply scientific fact.
Hwites do not understand what it means to relate to the land as stewards rather than as masters, and cannot imagine (or are incentivized not to imagine) a solution other than "what if we just kept murdering but only hurt the bad guys this time". Dexter-ass "traditions".