I'm going to intentionally try to keep my mutual friends apart
Why do you want to keep them away from each other?
I'm afraid if they start dating, I will lose my current girlfriend.
I'm sorry you feel that may happen, but that doesn't make what you want to do okay.  People shouldn't manipulate others, even if they fear something bad might happen if they don't.  You should talk this out with your friends and your girlfriend to make sure what you're worried about doesn't happen.
I'm not going to do that, they lives their lives and I will live mine. Besides, I will look like an insecure person. I don't need that.
But you are acting insecure by trying to manipulate others. Only a few words can do the trick and maybe treat your girlfriend better so she won't break up with you.