To reproduce:

        public RadForm1()
        {
            InitializeComponent();

            DataSet ds = new DataSet();
            DataTable dt = new DataTable();
            dt.TableName = "Tasks";
            dt.Columns.Add("Id");
            dt.Columns.Add("ParentID");
            dt.Columns.Add("Title");
            dt.Columns.Add("Start", typeof(DateTime));          
            dt.Columns.Add("End", typeof(DateTime));
            dt.Rows.Add("1", "", "Item1", new DateTime(2018,03,16), new DateTime(2018,03,20));
            dt.Rows.Add("2", "1", "child", new DateTime(2018,03,16), new DateTime(2018,03,17));
            dt.Rows.Add("3", "", "Item2", new DateTime(2018,03,16), new DateTime(2018,03,20));
            ds.Tables.Add(dt);

            this.radGanttView1.GanttViewElement.TaskDataMember = "Tasks";
            this.radGanttView1.GanttViewElement.ChildMember = "Id";
            this.radGanttView1.GanttViewElement.ParentMember = "ParentId";
            this.radGanttView1.GanttViewElement.TitleMember = "Title";
            this.radGanttView1.GanttViewElement.StartMember = "Start";
            this.radGanttView1.GanttViewElement.EndMember = "End";
            this.radGanttView1.GanttViewElement.DataSource = ds;
            this.radGanttView1.Columns.Add("Start");
            this.radGanttView1.Columns.Add("End");            
            this.radGanttView1.GanttViewElement.GraphicalViewElement.TimelineStart = new DateTime(2018,03,10);
            this.radGanttView1.GanttViewElement.GraphicalViewElement.TimelineEnd = new DateTime(2018,03,31);
            //"child" item is readonly
            radGanttView1.Items[0].ReadOnly = true; 
        }

Workaround:

        public class CustomBaseGanttViewBehavior : BaseGanttViewBehavior
        {
            protected override void ProcessMouseDownOnTaskElement(GanttGraphicalViewBaseTaskElement element, MouseEventArgs e)
            {
                GanttGraphicalViewBaseItemElement taskItem = element.Parent as GanttGraphicalViewBaseItemElement;
                
                if (e.Button == MouseButtons.Left && !taskItem.Data.ReadOnly)
                {
                    base.ProcessMouseDownOnTaskElement(element, e);
                }
            }
        }