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I've heard though unreliable sources that it's the nirvana fallacy, list of logical fallacies:
solutions to problems are rejected because they are not perfect.
Although, this doesn't quite fit. I've really only heard an appeal to futility called a logical fallacy in vegan spheres. So I question the validity about if and how it constitutes a logical fallacy. References would be great!
Related question
Are there any notable works that touch on pursuing a moral good that is likely futile?
Yes, it's different from the nirvana fallacy. The nirvana fallacy is: "X is the ideal perfect goal; Y is a proposed solution that fails to completely achieve X; therefore Y is not worth doing." e.g. "World peace would be ideal; this peace treaty fails to completely achieve world peace; therefore this peace treaty is not worth doing."
The fallacy you call "appeal to futility" is, "X is the ideal perfect goal; there is no possible perfect solution Y that completely achieves X; therefore X is not worth attempting." e.g. "World peace would be ideal; there is no conceivable peace treaty or other action that would completely achieve world peace; therefore, there's no point in working towards world peace."
It's fallacious, yes. Although a goal may not be achieved fully, there can still be value in striving for it, because the effects of doing so are good. For a simple example, when we shoot arrows on a range we aim for the perfect center of the target. We're never going to hit the absolute perfect center, which is a point of 0 size, but trying to hit the perfect center helps us to get closer to it and shoot more accurately.
Many logical fallacies are only fallacies in specific circumstances. Appeal to futility is only a fallacy if the situation is not actually futile. If the situation is (apparently) futile, the Best answer is to save your resources for another problem.
