I would like to be able to not allow the user to change the state of the checked state in a checkedtreeview. Is there any way to do that? I.e. if the user clicks the checkbox, it is ignored for specific nodes.

If you are using the SF CheckedTreeView, then the only option you have at the moment.  This control was added to extend this type of functionality.  You may just want to use a regular TreeView control and turn on check boxes.