How far does being "open-minded" go?

Where do you draw the line between open-mindedness and foolishness?

Essentially, this question was inspired by me being accused of being close-minded because I don’t believe people who believe they are part animal actually are. “Just be more open-minded” I’m told.

In order to be “open-minded” are we to reject scientific principles and accept things that lack evidence? Are we just supposed to accept everyone’s experiences and interpretations of those experiences fact because they said so? Where is the line drawn?