Is it normal that step family shouldn't be considered family?
I don't think stepparents, stepchildren, and stepsiblings should be considered family. The people that should be family to you are: your parents, siblings (bio or adopted), your children (bio or adopted), as well as uncles, aunts, grandparents, cousins, nieces, nephews, pets, and friends (friends are the family you choose). Step-anything should never count.