I really don't care about visual similarity. For me it's more about getting the character and plot right. Except for possibly adding humor where it is lacking in the original, or spoofing the original for a proper parody, they need to get the feel of the original right in the same way as when it is taken from one medium to another, or is remade
well. (Most American remakes of European films are crap because they don't get the original feel right. It has nothing to do with the actors looking different, although the fact that American actors mostly look like cloned photo models instead of individuals obviously doesn't help. Precisely because it changes the feel.)
For example, starting with Star Trek - The Original Series, the novels based on it as well as Star Trek - The Animated Series keep the essence of the original, and so do many fan productions of new Star Trek episodes even if they don't look right. I once saw a Star Trek porn parody. Something like that could be good, but it was crap because they didn't get the feel of the original at all. (Plus it was bad porn, too.)
Of course if the original is very much about visual style, then you need to get that right as well. I guess an example for this is Totally Spies! and its parody Paprika Trainer. (A pretty good game for playing as a game and a parody, not really for porn.)
But in general, you can change a lot of things and even replace all the characters and still have a good parody.
Lust Academy is probably the best Harry Potter parody, even though its setting is a magic school in America and basically the only visual resemblance to the original is the unavoidable Emma Watson lookalike classmate.