Conditional replace accented characters with non-accented ones

Try:

Sub Demo()
Application.ScreenUpdating = False
Dim StrFnd As String, Rng As Range, i As Long, j As Long
StrFnd = "03AC 03B1 03AD 03B5 03AE 03B7 0390 03B9 03CA 03B9 03AF 03B9 03CC 03BF 03CD 03C5 03B0 03C5 03CE 03C9"
For i = 0 To UBound(Split(StrFnd, " ")) Step 2
  With ActiveDocument.Range
    With .Find
      .ClearFormatting
      .Replacement.ClearFormatting
      .Replacement.Text = ""
      .Forward = True
      .Wrap = wdFindStop
      .MatchWildcards = True
      .Text = "<" & ChrW("&H" & Split(StrFnd, " ")(i)) & "*>"
      .Execute
    End With
    Do While .Find.Found = True
      Set Rng = .Duplicate
      With .Duplicate
        .Start = .Start + 1
        For j = 0 To UBound(Split(StrFnd, " ")) Step 2
          If InStr(.Text, ChrW("&H" & Split(StrFnd, " ")(j))) > 0 Then
            Rng.Characters.First.Text = ChrW("&H" & Split(StrFnd, " ")(i + 1))
            Exit For
          End If
        Next
      End With
      .Collapse wdCollapseEnd
      .Find.Execute
    Loop
  End With
Next
With ActiveDocument.Range
  With .Find
    .ClearFormatting
    .Replacement.ClearFormatting
    .Replacement.Text = ""
    .Forward = True
    .Wrap = wdFindStop
    .MatchWildcards = True
    .Text = "<" & ChrW("&H03B5") & ChrW("&H03CD") & "*>"
    .Execute
  End With
  Do While .Find.Found = True
    Set Rng = .Duplicate
    Rng.Start = Rng.Start + 1
    With .Duplicate
      .Start = .Start + 2
      For j = 0 To UBound(Split(StrFnd, " ")) Step 2
        If InStr(.Text, ChrW("&H" & Split(StrFnd, " ")(j))) > 0 Then
          Rng.Characters.First.Text = ChrW("&H03C5")
          Exit For
        End If
      Next
    End With
    .Collapse wdCollapseEnd
    .Find.Execute
  Loop
End With
Application.ScreenUpdating = True
End Sub