Instead of sitting there trying to pick a side, I think you should some how have both friends to sort through your problems with you there to help them, like a true friend. Explain to them what their fight is doing to you and that they are being selfish making you pick sides maybe that way you can make them understand how silly they are being. When you get them to talk to each other, you can explain each of their wrong thoughts to them in a way that would get them to understand and calm down. Be there for them as much as you can.
Mr. Swag