As a Teacher, you have full control of your class. It is up to you what access you would like parents to have. You can configure the settings for your class by clicking on "Class Settings".
Here's what you should see:
Here's the definition for each setting:
Enable Daily Summary: All connected users in the classroom will receive a daily summary email with upcoming activities happening in the classroom and scheduled commitments for the day.
Allow parents to create activities and announcements: Parents will be able to create announcements, events, to-do lists, volunteer requests and share it with all users connected to the classroom.
Allow parents to comment and add reactions to announcements: Parents will be able to add comments and reactions on announcements posted to the classroom page. Comments and reactions are visible to all users.
Allow parents to upload photos and files: Parents will be able to share photos and files as a private message to connected teachers in the classroom as well as upload photos and files to announcement comments.
Allow parents to start conversations with other parents: Parents will be able to private message all parent & family members connected to the classroom directory.
Show the classroom directory to parents: Parents will be able to see all parents & family members connected to be classroom.
Show the class supply list: All users connected to the classroom page will see the supply list on the classroom page. If there are any active supply lists, parents will be able to purchase items.