My take is slightly different, but unsurprisingly it's closer to @Bullen's. What I think constitutes the "low standard" is that hunting is fun and meat is tasty, so the incentive to rationalize this behavior is very high and the incentive to look for alternatives is very low.
In principle though, I'm not opposed to particular animal products, but rather to the conventional means of producing them. If you found a dead deer and turned it into venison, I don't have any objection to that.
On the specific situation of overpopulation, I'm not a utilitarian, so I'm probably opposed. If it were extremely well targeted to eliminating only the animals in extreme states of distress with no hope of recovery, I'd feel differently. However, killing perfectly healthy animals for the good of the many is too close to moral reasoning that has justified many human atrocities for me to buy in.