We do not allow you to stop 2 way messaging, however, you can do the following - 

• Use POSTS, ANNOUNCEMENTS, and ALERTS to communicate updates
• Turn off notifications of messages by going into Account Settings > Notifications
  
• Set Quiet Hours by going into your Account Settings. 
  • By doing so even if parents message you, they will know that you have quiet hours set and will not respond.
• Tun off Comments on updates by going to you Class Settings > Parent Permissions
  • When you do this at the class level the parents cannot comment on your posts, announcements or alerts.
  • You can also turn off comments only for a particular post/announcement/ alert by clicking on the No comment icon in the post creation form.

Additional Resources:

• Notification Settings - Quiet Hours