Here is an updated version which, I believe, works (note also that I updated the DynamicModule version in the previous poste since it was not quite correct and did not work). Note both the use of the Deployed -> True option so that the content of the Manipulate is not selectable and also adding a Dynamic around the Line graphics directive. In essence I am forcing the Manipulate to behave exactly like the DynamicModule in the earlier (edited) posting. My guess as to why your original Manipulate did not work properly is that it is trying to create internally a LocatorPane. However, the Enabled option to LocatorPane only applies to all of the locators at once: there is no fine-graned use of Enabled in the LocatorPane which can restrict it to a selected subset of the locators. A WRI developer can perhaps comment....

Manipulate[
 Graphics[{
   Locator[Dynamic[p1], Enabled -> move],
   Locator[Dynamic[p2], Enabled -> ! move],
   Dynamic@Line[{p1, p2}]},
  PlotRange -> 1.1,
  Background -> White],
 {{p1, {0, 0}}, ControlType -> None},
 {{p2, {1, 1}}, ControlType -> None},
 {{move, False}, {False, True}},
 Deployed -> True]

Though I am not sure why you are seeing the behavior in Manipulate that you indicate (it appears to be a bug but others should chime in) here is an example of an implementation using DynamicModule [I have updated this code from an earlier version which did not work properly]:

Deploy@DynamicModule[{p1 = {0, 0}, p2 = {1, 1}, move = False},
  Panel@Column[
    {Checkbox[Dynamic[move]],
     Graphics[
      {Locator[Dynamic[p1], Enabled -> Dynamic[move]],
       Locator[Dynamic[p2], Enabled -> Dynamic[! move]],
       Dynamic@Line[{p1, p2}]},
      PlotRange -> 1.1,
      Background -> White]}]]

And, if you want this to be within a Manipulate, you can do something like this:

Manipulate[

 Graphics[{
   Locator[Dynamic[p1], Enabled -> move],
   Locator[Dynamic[p2], Enabled -> ! move],
   Line[{p1, p2}]}, PlotRange -> 1.1, Background -> White],

 {{p1, {0, 0}}, ControlType -> None},
 {{p2, {1, 1}}, ControlType -> None},
 {{move, False}, {False, True}}]