To reproduce:
- set IsReadOnly to true
- hold down the left mouse button and try to select some area => the selection will appear when you release the button

Workaround:
     radRichTextBox1.Document.Selection.SelectionChanging += Selection_SelectionChanging;
            radRichTextBox1.Document.Selection.SelectionChanged += Selection_SelectionChanged;
        

        void Selection_SelectionChanged(object sender, EventArgs e)
        {
            radRichTextBox1.IsReadOnly = true;
            
        }

        void Selection_SelectionChanging(object sender, EventArgs e)
        {
            radRichTextBox1.IsReadOnly = false;
        }

Resolution: 
This issue is addressed in the new version of the control - RadRichTextEditor. Please use the new control instead the RadRichTextBox.