the Orb guild had a house near a DoC member, and we spent many nights fighting them. It got to the point that we showed a mutual respect for the fights we had. At least this was my perspective. There was an alliance that was formed between us when we fought on the field. I've never mandated that a certain guild is "off limits" frankly if you dont have a DoC tag above your head, you're not in my guild. As I said, DoC was made up of a lot of soloist, which all made friends with other guilds, as you sometimes need help with certain aspects UO. You would often find a non DoC member running with a group of DoC members, because they had formed some sort of relationship with a DoC member. A few members of Orb joined their tamers in DoC. That was pretty much the extent of the DoC and Orb connection. My loyalty to my guild only falls on the characters who have the tag above their head. If a person who had a character in DoC, they were only in DoC when they played that character.
I cant answer what an Orb member would do or not do. Most likely they would be farming/taming on a DoC and run PvP on an Orb char. I havent been active in over 3 years, so what's happened within that time, I cannot attest to.