The main difference is that "Why is the skin red?" refers to specific skin, and would most likely be some skin brought up previously in the conversation ("my skin" or "your skin") but possibly the skin of something that you've been talking about before ("the skin of the apple" if you've been talking about an apple); whereas "Why is skin red?" implies that skin in general is red. Both can be 100% correct.
I answered "Why is skin red?" and it was accepted (July 17 2020.) "Why is skin red?" would mean skin generally (all skin by default), not any specific skin; thus it would be strange for someone to say that in English, because the premise of the question, that skin (in general) is red, is a false premise. But grammatically it is perfectly correct, and since Duolingo has dancing dogs, frogs that do the dishes, etc., it is no surprise that skin would generally be red by default for some of these sentences.
Perhaps another thing that could go against that translation is that it's more common to use 는 than 이/가 when referring to something in general. But from my understanding it's not necessarily wrong; if someone has already brought up the topic of skin as a general topic, then I don't think you need to use 는 even if you're talking about skin in general. (But as for that point, it would be better to ask a native Korean speaker. I can explain the nuances of English much better than Korean.)