What to do when your new best friend's friend is the person you loathe immensly?

You have to look at yourself, the relationships involved and be honest with yourself about what you find. Why is your new best friend your new best friend? What do you have in common, why are you connected? Why do you loathe the other person? What have they done or said to cause this? IF the two of them are friends, they must have some common interests, some reason they like each other and choose to be around each other. If you can find out what their common interest is, this may give you something in common with both of them and you may find that you don't loathe the other person as much as you thought. You might find that maybe you need to rethink your opinion of the other person