Compare the two solution sets below: in the first one (`x == False`), there are only 3 dependent variables while in the second one (`x == True`), a dependent algebraic variable is introduced as `r[t] == 5` (converting the ODE to a DAE). A DAE often requires a different `NDSolve` method, here I used `"EquationSimplification" -> {Automatic, "SimplifySystem" -> True}` which messes up the solution order as is apparent from the plots.

    ClearAll[t, R, A, P, r, x];
    eq = {
          R'[t] == -.1 R[t],
          A'[t] == .1 A[t],
          P'[t] == 0,
          If[x, r[t] == Sin[t], Nothing],
          R[0] == 1, A[0] == 1, P[0] == 1
      };
    
    sol1 = Block[{x = False}, 
       NDSolve[eq, {R, A, P}, {t, 0, 20}, DependentVariables -> {R, A, P}]];
    sol2 = Block[{x = True}, 
       NDSolve[eq, {R, A, P, r}, {t, 0, 20}, DependentVariables -> {R, A, P, r}, 
        Method -> {"EquationSimplification" -> {Automatic, 
            "SimplifySystem" -> True}}]];

    Grid[{
       LogPlot[#[t] /. sol1, {t, 0, 20}, PlotLabel -> #] & /@ {R, A, P},
       LogPlot[#[t] /. sol2, {t, 0, 20}, PlotLabel -> #] & /@ {R, A, P, r}
    }]

![Mathematica graphics](https://i.sstatic.net/fWHbj.png)

Can anyone reproduce this bug?

(Mathematica 10.4.0.0, Windows 7, 64bits)