How to find all the positions of max value of a list efficiently?

A fast uncompiled alternative without pattern matching is to use the NonzeroPositions property of SparseArray, as long as you're dealing with numerical data.

list = RandomInteger[{1, 100}, 10^7];

SparseArray[Unitize[list - Max[list]] - 1]["NonzeroPositions"]; // RepeatedTiming
(* 0.0855 *)

Position[list, Max[list]] // RepeatedTiming
(* 0.509 *)

compPos[list, Max[list]] // RepeatedTiming (* Marius' solution *)
(* 0.0366 *)

SparseArray[Unitize[list - Max[list]], Automatic, 1][
   "NonzeroPositions"]; // RepeatedTiming (* MichaelE2's solutions *)
(* 0.0663 *)

For a 1D list you can also use

Pick[Range@Length@list, list, Max@list]

For a one-dimensional list:

compPos = 
 Compile[{{list, _Integer, 1}, {max, _Integer}},
  Block[{copy = list, i = 1},
   Do[
    If[
     list[[j]] == max, copy[[i++]] = j],
    {j, Length[list]}];
   copy[[1 ;; i - 1]]
  ], 
   CompilationTarget -> "C"
  ];

Though I think Position is a good non-compiled alternative in this case, since the "pattern" you use is a number. There won't be any useless matches to this pattern.

Performance Test

list = RandomInteger[{1, 100}, 10^7];
Position[list, Max[list]] // AbsoluteTiming // First

0.8220470

compPos[list, Max[list]] // AbsoluteTiming // First

0.0830048

Obviously, 10 times speed-up