Every work that I teach in both my 9th grade and AP Language classes is listed on the syllabus that I hand out at the beginning of the year. All a parent has to do is google the book title to see if there is anything they might consider sensitive or objectional. 

For example, the Wikipedia article on The Catcher in the Rye contains an entire section about its controversial nature. If a parent was still concerned after reading the article, any teacher would be happy to provide them with a copy so that they could read it for themselves or opt out of the book.  When I was in high school (at a Virginia school) and my mother saw the syllabus, she asked me to bring home a copy of Catcher in order for her to do just that. She read the book and determined that it would be fine for me to read. 

I know of no teacher, principal, or school district that would force a student to read something that their parents do not want them to read. However, it is up to the parents to actually read the syllabus they sign at the beginning of the year and talk to the teachers about the content. 

Also, while the focus of this discussion has been on works in English class, the vague language could include criteria from all subjects. An article about global warming in an environmental science class could be "sensitive." A reading about socialism in history class could be construed as "promoting" it and therefore is "sensitive." Discussing current events topics in journalism or government class could be considered "sensitive." 

Teachers want parents to take an active role in their child's education. However, the parent right to decide what their child reads has to be coupled with the responsibility to do research about the works. You cannot have one without the other, since it is impossible for a teacher to predict what any one of their 100+ students may find "sensitive." 

If this amendment passes, I will need to mark everything on my syllabus as "sensitive," including the "classics" that so many of the comments have been praising.