I don’t think the phrase “real vegan cheese” is linguistically clear in any way. Is the “real” about the “vegan” part, the “cheese” part, or the “vegan cheese” part? I.e. “real dog food” has nothing to do with the realness of the dogs, it’s about the “food”. But then in the sentence “real prada bag” the “real” is about the “prada” portion not about the “bag” portion. “Real” can modify either the modifier or the noun.

“Really” makes the sentence more clear, because it adds emphasis to the “vegan” modifier on “cheese” - it wouldn’t apply to the “cheese” part directly. I.e. in the sentence “really big cheese” the “really” is clearly adding emphasis to the “big”.