To reproduce:

public Form1()
{
    InitializeComponent();
    this.radRichTextEditor1.IsReadOnly = true;
}

Workaround:
private void Form1_Load(object sender, EventArgs e)
{
    this.radRichTextEditor1.IsReadOnly = true;
    Telerik.WinControls.RichTextEditor.UI.DocumentWebLayoutPresenter webLayoutPresenter = 
        this.radRichTextEditor1.RichTextBoxElement.ActiveEditorPresenter as Telerik.WinControls.RichTextEditor.UI.DocumentWebLayoutPresenter;
    webLayoutPresenter.Caret.Width = 0;
}