I came here to ask the same question and see if there was a better solution than the one I already have - which is basically the same as the one outlined by @tmbb. I created a helper combinator for it which may help others searching for the same answer. Note my version assumes ASCII input only since that fits the problem domain I am working on.

  def anycase_string(string) do
    string
    |> String.upcase
    |> String.to_charlist
    |> Enum.reverse
    |> char_piper
    |> reduce({List, :to_string, []})
  end

  defp char_piper([c]) when c in ?A..?Z do
    c
    |> both_cases
    |> ascii_char
  end

  defp char_piper([c | rest]) when c in ?A..?Z do
    rest
    |> char_piper
    |> ascii_char(both_cases(c))
  end

  defp char_piper([c]) do
    ascii_char([c])
  end

  defp char_piper([c | rest]) do
    rest
    |> char_piper
    |> ascii_char([c])
  end

  defp both_cases(c) do
    [c, c + 32]
  end

utf8_char([?n, ?N])
|> utf8_char([?a, ?A])
|> utf8_char([?m, ?M])
|> utf8_char([?e, ?E])

You can also define your own combinator (case_insensitive("name")) that returns the above.