Thinking about this the other day, it occurred to me that the some-of-my-best-friends argument is dismissed because it is misunderstood. It is not an all-purpose defense; it is generally used in a specific case.
Here's an example. Bill is gay. John isn't. John says something to Bill. Bill finds it offensive, and says so. Would John use the some-of-my-best-friends response here? Well, he might — never underestimate stupidity, ineloquence, and blind panic — but probably not: it doesn't make sense in such a case. If a gay man is standing in front of you, telling you that he is offended, it does no good to mention the existence of some of your gay friends. There is no reason for him to give a damn.
Now consider this one. Simon and Harry are both white. Simon says something that Harry considers to be racist towards black people, and Harry says so. Simon might well respond to Harry that he has lots of black friends — and it does make sense to do so. This is exactly the sort of situation where the some-of-my-best-friends argument usually occurs: when dealing with people who are offended on the behalf of others.
Considering that, it becomes clear that the some-of-my-best-friends argument is in fact a shorthand.
Some of my best friends are black
Some of my best friends, unlike you, are black, and I don't have to watch my mouth around them, and they, unlike you, don't think I'm a racist
or, more to the point:
You claim that what I say is deeply offensive to black people, but when I say it in front of actual real-life black people, they don't see it as a reason not to be my friend.
After all, the alternative simply makes no sense:
Some of my best friends are black, but I'm careful not to express my opinions in front of them 'cause if I did they'd hate me.
I think this much-scoffed-at argument may have a lot more weight than the scoffers realise.