A guild can only have its allegiance pledged to a single faction, even if it has members who have no characters in that faction. A character can only participate in PvP with a guild that is the same faction as the character. This may be better explained with some examples.
Let's say a player has two characters: Elf, an AD character, and VanNord, an EP character. He has joined two guilds "AD Rules" (AD) and "Mead Guild" (EP). Here's what we know:
- Elf and VanNord cannot be in the same campaign.
- Elf can be in a campaign with AD Rules, but not Mead Guild.
- VanNord can be in a campaign with Mead Guild, but not AD Rules.
- Obviously, AD Rules and Mead Guild should be able to be in the same campaign; it'll be a nightmare to ensure all members are "compatible".
My conclusion from the above four points is that AD Rules and Mead Guild can be in the same campaign, but the player has to decide whether to play as Elf or VanNord in that campaign, while the other character must join another campaign. However, there's probably nothing that prevents the player from communicating with both guilds while participating in the campaign.