You argued, "protecting albino animals would be endorsing a rare genetic anomaly that could lead to other long-term problems in the local deer population." Your argument is valid only if protecting albino animals actually leads to other long-term problems in the local deer population. The facts, however, do not support your theory as the albinism trait and its associated problems die with the white deer unless it successfully mates, which is unlikely unless three factors occur. Instead, hunting deprives a natural predator of its prey and assures the destruction of the white deer.
First, the white deer young must survive long enough to reach maturity. You note that "[a]lbino animals lack pigments in their eyes and skin; thus, they are more susceptible to other problems such as vision loss and skin lesions." In other words, white deer young are more susceptible to death from natural predation and illness than their non-albino brethren. Thus, young white deer are less likely to reach maturity, and as young deer, albino or not, may not be hunted, hunting adult white deer does not affect prevent any suffering of the young white deer.
Second, to propagate the white deer gene and its associated anomalies, the adult white deer must survive long enough to mate. You note that "[a]lbinos  suffer much higher natural mortality rates because they are much more visible to predators." Because of their vision problems, white deer are also less likely to see natural predators and if in addition are ill, as you stated, the white deer is too weak to flee danger. With this triple hazard to their lives, the white deer are more likely to die of natural predation, and are less likely to survive long enough to mate, even without hunting.
Third, the white deer must actually mate to propagate the trait. As you noted "[a]lbinism is a recessive genetic trait." As you may recall from genetics, two genes are present in each deer for color, each parent contributes one gene, a white deer carries two recessive albinism genes, and a normal appearing deer may carry one albinism gene and one normal gene, or carries two normal genes. Thus, a white deer mating with any deer would cause the fawn to carry at least one of the recessive white deer genes, i.e., nature as nature intended, but the odds of a white deer propagating another white deer depends on the prevalence of the recessive white gene in the deer population.
Based on the statistics of recessive genetics, and that according to one Facebook post there are only six white deer in the park (or less, now that one was shot and killed), I believe that less than one in sixty-four (64) deer in the general population of the park carry one of the recessive white deer genes. (Perhaps you have actual statistics?)
As such, the probability of a white deer mating with another deer and propagating a white deer fawn is 1/64 times 1/4 (the recessive cross mix), or one in two hundred fifty-six (256). This 256 number assumes that a white deer is just as likely to survive to maturity and is equally likely to mate as a normal deer.
Both of these assumptions, however, are likely false and overstate the odds. As you noted, a white deer is less likely to survive to maturity and to mate. Include that defective (vision loss) and ill (skin lesions) animals are generally shunned from mating, the likelihood of a white deer mating is less likely, which means that a white deer is unlikely to propagate its long-term problems in the local deer population.
Lastly, your arguments imply that white deer hunting aids nature. Humans, however, are the only predators capable of seeing deer with magnification and killing them without bodily contact, i.e., with guns or arrows from afar. As the white fur of the white deer increases the likelihood that a hunter would see an adult white deer, and their poor eyesight and health decrease their chance of escape, allowing white deer hunting assures a 100% kill. This kill then deprives a natural predator of its prey, and forces the natural predator to kill another animal perhaps not as defective or ill. Consequently, the hunting of white deer interferes the natural predation in the park, and with their very low numbers, unnecessarily ensures their destruction.
In summary, allowing the hunting of white deer does not affect "other long-term problems in the local deer population," interferes with the usual deer predators, and unnecessarily ensures their destruction. Thus, your arguments against protecting white deer from hunting are unfounded. Please reconsider, and ban the hunting of white deer. Thank you.
Gerald R. Prettyman