Then we agree on most of the problem. With regard to the disease and such: Blackirish asks:
They were going to move this deer to a shelter less then a mile away in IL. This spreads disease how?
In logic and critical thinking, a slippery slope is an informal fallacy. A slippery slope argument states that a relatively small first step leads to a chain of related events culminating in some significant effect, much like an object given a small push over the edge of a slope sliding all the way to the bottom.
In this case, the deer could traverse the whole country by being moved just a mile between adjacent shelters. I do not want to play a veterinarian here, so I do not know much about complications of moving sick animals - and as I said, the law already forbids such transportation without an explicit approval. There is no obvious gain from such transportation, but there is a chance of loss. It is wise to not transport. It is humans' responsibility to do what is best for the population, even if some specific individuals have to die. We are not Pak Protectors.
Do you seriously think it would be more merciful to allow the fawn to starve to death?
It's a serious philosophical question. It's not guaranteed that the fawn will die, but it's highly probable, especially if it still depends on milk. On the other hand, there is no reason to kill the fawn - it's not likely to run farther than an adult deer. What is gained by killing the deer? What is lost by releasing it?
(There are obvious philosophical similarities with human children, where expecting mothers are told by learned doctors that the child won't be healthy, and it's better to kill him here and now, before the child is born. The living beings are different, but the moral problem is of the same nature - taking direct responsibility for death of a young and defenseless living being.)
You can also look at it from another angle. What if no human ever saw the fawn? Then there would be no interference. If the workers of the shelter "acted stupidly" and brought a wild creature in, they have a perfectly good way to repair the damage: take the fawn and put it back exactly where it was found. Leave him there to his fate. It would be fair. I don't think the fawn would be any better from that, but the humans would be better off because they did all they could. That is important. All human conflicts begin in human mind. It is very wise to be nice to others, be it humans or animals. Everyone probably knows that now, after the GZ trial; but all the religious literature (with one exception) tirelessly repeats this very idea.
I think your argument falls apart with the slippery slope argument because that leads to absurdities like this or worse an excuse for government to use military force just because it can. Mark Styens theory of a governmental so big it becomes a “blind leviathan” unaccountable bureaucrats serving the bureaucracy not us. It leads to a child eating a pop tart and being deemed a threat because it looks like a gun. Or using a task force and drones to kill a baby deer.