Family members tend to have two basic issues with polyamory. One seems to be an attack on what they see as some basic family values. For Monster's case, they may see it as wrong for a person to persue another man's wife. (I hate to say stuff like that because it implies ownership, but that is the standard view of relationships today -- one of ownership of each other.) If this is the case, you can engage philosophically with them on this (which rarely convinces people unless they are logical by nature). More relaistically, I think they will have to weigh their objections to this verses their desire to stay in touch.
The other issue is usually worry that the person is in for a let down. They may want him to end it now instead of getting hurt later on (because they can not really forsee it working out). If this is the case, then I think family members will come around when they see that Monster is happy over a long period of time.
Without knowing the exact objections that Monster is getting, it is hard to say what will help.