I'm kind of torn on that story. She shouldn't have been fired but......
Based on my experience, 5 your olds have very fixed ideas about the binary of sex and gender and they are very certain of the binary. My boy tends to grow his hair long. At about 5 he had short hair and his 5 year old cousin saw a picture of him as a 4 year old with long hair, "That's you when you were a girl!" Far more common an attitude among fiver year olds than not from what I've seen. Also, 5 year olds occasionally identify as cats, dogs, dragons......