Both Earth 1 and Supergirl’s Earth have Batman, and while we’ve never seen Vixen on Supergirl’s Earth, that doesn’t mean she doesn’t exist. Also, to the original point, Obama could have simply been president a term earlier... Or he could have just lost his second term...

Well, they’ve already got Roy Harper and Wally West, and they’ve dropped several Nightwing easter eggs, so it wouldn’t be that far of a stretch storywise. I do worry that they wouldn’t have the budget for a character like Beast Boy or Starfire, though.