I am assuming that you are referring to the second section in Chapter 10 in your question. The three events in this section that show that people are starting to mistrust Stargirl involve her unorthodox version of the Pledge of Allegiance, her attendance at the funeral of someone she didn't even know, and her kindly meant but unappreciated act of buying a new bike for a child who had been in a cycling accident.
Stargirl had been overheard reciting her own version of the Pledge of Allegiance, and a copy of the words she says appears one day on the student bulletin board on campus. A possibly but not certainly mean-spirited note attached to the copy with the words, "This is how she says the Pledge of Allegiance." All the students know who the note is referring to, and reaction to the post is mixed but not necessarily negative. Still, this is the first indication that public opinion towards Stargirl is changing.
A second incident described in the chapter indicates with certainty that people are beginning to be offended by Stargirl's innocent but unorthodox behavior. Stargirl attends the funeral of someone she does not even know, empathetically crying with the mourners and mixing with the family afterwards. When the distraught daughter of the deceased realizes that the unfamiliar attendee did not even know her father, she confronts Stargirl and rudely throws her out of the house.
In the third incident described in the chapter, a young boy is injured while riding his bike; he develops complications and is hospitalized for a period. When he comes home, there is a large gathering to welcome him, and a brand new bike of unknown origin. The bike ends up being the focus of great friction among the boy's family members, and although they never do discover who the giver of the bike is, students at Mica High are pretty sure it is Stargirl. Stargirl, marching to the beat of her own drummer, so to speak, acts with good intentions, but does not realize that her unconventional acts are not always taken kindly by others (Chapter 10).