Deleting duplicates of a list without touching specified elemets

This should be reasonably fast:

ClearAll[value];
value[exceptions_List] := value[Alternatives @@ DeleteDuplicates@exceptions];
value[exceptions_][x_] /; MatchQ[x, exceptions] := Unique[];
value[exceptions_][x_] := x;

OP's examples:

list = {1, 3, 5, 5, 12, 12, 6, 11, 7, 7, 9, 10, 2, 2, 4};
positions = {3, 9};
DeleteDuplicatesBy[list, value[list[[positions]]]]
(*  {1, 3, 5, 5, 12, 6, 11, 7, 7, 9, 10, 2, 4}  *)

list = {1, 2, 3, 3, 4, 3};
positions = {3};
DeleteDuplicatesBy[list, value[list[[positions]]]]
(*  {1, 2, 3, 3, 4, 3}  *)

---

Update. Even faster:

ddxc[expr_, exceptions_List] := Module[{value},
   (value[#] := Unique[]) & /@ exceptions;
   value[x_] := x;
   DeleteDuplicatesBy[expr, value]
   ];

SeedRandom[0];
list = RandomInteger[1000, 10^5];
positions = Range[100];
DeleteDuplicatesBy[list, value[list[[positions]]]] // Length // AbsoluteTiming
ddxc[list, list[[positions]]] // Length // AbsoluteTiming
(*
  {0.661751, 10668}
  {0.136582, 10668}
*)

Clarifiation: The performance concern regarding Unique appears to no longer apply in recent versions. The code below still tests faster for me but deprecation of methods using Unique is presently unfounded.

---

This question is related to How to Gather a list with some elements considered unique and I propose a similar solution to what I offered there.

fn1[a_, p_] :=
  Module[{f, x, i = 1},
    Scan[(f[#] := x[i++]) &, p];
    GatherBy[a, f][[All, 1]]
  ]

fn1[{1, 3, 5, 5, 12, 12, 6, 11, 7, 7, 9, 10, 2, 2, 4}, {5, 7}]

{1, 3, 5, 5, 12, 6, 11, 7, 7, 9, 10, 2, 4}

Compared to Michael's fastest function:

SeedRandom[0];
list = RandomInteger[1*^6, 2*^6];
positions = Range[100];

fn1[list, list[[positions]]]  // Length // AbsoluteTiming
ddxc[list, list[[positions]]] // Length // AbsoluteTiming

{2.90443, 865482}

{7.5404, 865482}

DeleteDuplicates[list, And[#1 == #2, Not@MemberQ[list[[positions]], #1]] &]