What is the last step an educator can take to convince a parent to allow their child to read a particular book?

If I were in this situation, I think I would encourage the parent to read the book along with their child. Maybe the reasons they have for opposing it are opinions from other people who have read the book; if they read it and get the chance to discuss it with their student while that student is also reading it in class, perhaps they would feel more comfortable with the material. They could also read it before their kid has the chance to so they can then make the final decision. I would describe my rationale for the choice, show them what kinds of projects and analysis we'll be doing in class, and the main themes I want students to get out of it. If they see what the main focus points will be maybe they will realize that the material that they were uncomfortable will be explained or taught in a way that doesn't shock students, just informs and teaches in a way that lets them come up with their own interpretations of the work. I'm guessing the department would have to approve the book anyway so letting parents know it's on the list of acceptable books for the school they may change their minds.