Can a step parent take out a life insurance policy on a child without the knowledge or consent of the biological parent?

This depends on the legal status of the step parent. If they are a legal guardian then I would say that yes they could. I'm sure there must be much more to this story. If you are a stepparent by marriage, you have no legal authority over the child in regards to obtaining life insurance or any other issues regarding the child's welfare. If you have been appointed legal guardian by the court, you have the right to do whatever is in the best interest of the child depending upon the terms of the guardianship.