@Stangdon's comment is, I think, the core of the right answer.
"Skin" in English can be either a countable or a non-countable noun.
As a countable noun, "one skin", "two skins", etc, it refers to the hide of an animal, after the animal has been killed and the hide removed from the body. Like, "He kept two bear skins hanging on the wall as hunting trophies." (You could talk about the skin of a human being, of course, if you killed someone and made a rug out of his skin. But that's getting kind of creepy.)
As a non-countable noun, "skin" refers to the thing in general, of a creature living or dead. You can say, "Bob has white skin." You wouldn't say, "Bob has A white skin", just "has white skin". It's not countable.
"Vietnamese girls like white skin" is ambiguous without context. It could mean that they like their own skin to be white, or that they like men with white skin. I'm guessing you mean the second. If so, you could also say, "Vietnamese girls like men with white skin". Note that "men" here is plural, because "man" is a countable noun. ("Man" can also be uncountable, if you are talking about the human race, like "Man has written history going back several thousand years." But here we're talking about individual male people.) So "men" is plural, but "skin" is uncountable, neither singular nor plural.