Should a boyfriend who loves his girl be willing to give up his friends if they are hurting their relationship?

If he believes this, then yes. However, if only 'she' believes this, then she has to convince him that it is true. Love should not mean having to "give up" anything. Love should show one that it is time to move on.... "giving up" something always implies reluctance. If the love is real there will be a readiness.... which is very different.