Appeal to consequence is a logical fallacy in which someone claims that because a belief has negative results, or even negative implications, therefore that belief is not true. For example, belief in gravity enables murderers to push their victims from a height, making their deaths look like an accident. That doesn’t mean gravity is false, or even that we shouldn’t teach gravity.
However, the moral and ethical implications of Evolution do raise a few alarm bells. There is a fundamental difference between human beings and animals, as most Evolutionists will actually admit as much. Yet under Evolution, this is illogical. All value is entirely subjective. Moral views are no more binding than preference for ice cream flavors. This renders the Evolutionist’s view contradictory. Essentially, most Evolutionists do not live as if they believed in Evolution. But if they don’t live according to their beliefs, do they really believe it?
When you have two conflicting views, there are only two logical approaches. The first is to figure out if it's possible to reconcile them. The second is to accept that one of them is wrong, figure out which one that is, and discard it. Now, this does mean this particular argument could backfire. It's possible that an Evolutionist might decide that, since they believe Evolution is true, they should become Nihilists. However, most human beings instinctively know that both morality and value are objective. Therefore, they must acknowledge that Evolution, given that it necessarily leads to Nihilism, is false.
Failing this, there are, of course, excellent reasons to believe that Christianity, not Evolution, is true. And indeed, it is recommended to learn these reasons on top of this. Nevertheless, the fact that Evolution naturally leads to the conclusion that you are no more valuable than the food on your plate should be repulsive to the sensible mind.