For example, a liberal Christian complained that her (honest!) Christian answer did very poorly, because people associated liberalism with atheism. This suggests that the best strategy isn't necessarily to honestly list what you believe, but to list what you think a typical member of the group involved believes.

It depends how you define poorly. Her answer demostrated something useful about inaccurate stereotypes of Christianity. If the goal of the whole exercise is to convince others that Christianity is right, then her answer might be good because it teaches people about their misconceptions about Christianity.