procedure TForm15.cxCheckBox1PropertiesEditValueChanged(Sender: TObject);
begin
  if cxCheckBox1.Checked then
  begin
    cxScheduler1.OptionsView.WorkDays := cxScheduler1.OptionsView.WorkDays + [cxDateUtils.TDay.dSunday]
  end
  else
  begin
    cxScheduler1.OptionsView.WorkDays := cxScheduler1.OptionsView.WorkDays - [cxDateUtils.TDay.dSunday]
  end;
end;

procedure TForm15.cxCheckBox1PropertiesEditValueChanged(Sender: TObject);
var
  I: Integer;
  needDays: TList<TDateTime>;
  currentDate: TDateTime;
  maxDate: TDateTime;
begin
  // оставляем все воскресенья для текущего месяца
  currentDate := StartOfTheMonth(Now);
  maxDate := DateOf(EndOfTheMonth(Now));

  // список дат для выделения
  needDays := TList<TDateTime>.Create;
  while currentDate <= maxDate do
  begin
    if DayOfWeek(currentDate) = DaySunday then
    begin
      needDays.Add(currentDate);
    end;

    currentDate := IncDay(currentDate, 1);
  end;

  // само выделение
  cxScheduler1.DateNavigator.BeginUpdate;
  try
    cxScheduler1.SelectDays(needDays.ToArray, True);
  finally
    cxScheduler1.DateNavigator.EndUpdate;
  end;

  FreeAndNil(needDays);
end;