My Girlfriend's Friend
This must be driving you nuts at the moment,huh? What kind of strain does this certain friend puts in your relationship with your girlfriend? Is this friend a 'she'? Assuming it's the same one you describe as being psychotic, on medication and a social disaster. Through your reference of her; I suppose, this friend of hers does not have many (true) friends.
Paulgc, this is my opinion and it is just that.
You love your girlfriend, obviously. And she likes this person. Could it be compassion or an ability to empathize with this friend of hers that she is able to embrace a friendship with her? It seems that you are unable to accept her (now) and appear to be afraid of her; in terms of her influence in your relationship? Maybe you are embarrassed by her presence? Or is it that you just don't trust your girlfriend's judgment enough?
There are many types of people with differing abilities. Your girlfriend may be the kind that tends to understand instead of discriminate others (as you put it, crazy people in the world).
We don't have to like ALL of our girlfriend's friends; we just have to make sure 'the friend' treats HER well, truly care and genuinely love HER as a friend.
I believe you already have the answer but still needs a little processing. Your question is: What do I do?
AS LONG AS her friend is not getting her to do things she shouldn't be doing and this friend of hers is not a harmful threat..
Let her have her freedom of friends, for her to shine; her space, for her to grow. Love: respect, support, understanding, and care always prevails.