You can't. After you've sided with a faction for that character, you can't change so whatever you have selected you're stuck with that one for the rest of the event. (You can side with different factions with other characters)

Damn Bungie -blam!-ing sucks. The only reason i sided with any faction was because it mentioned, once you change your faction you cant side with another for another week. They failed to mention you cannot change during a rally.