The code in your module is ok, but in Elixir data is immutable, each time you add or remove an item from the queue, a new queue is returned, so you have to rebind q to the result of Fifo.*

iex(2)> q = Fifo.new
{[], []}
iex(3)> q
{[], []}
iex(4)> q = Fifo.in!(2, q)
{[2], []}
iex(5)> q
{[2], []}
iex(6)> Fifo.in!("r", q)
{["r"], [2]}
iex(7)> q = Fifo.new
{[], []}
iex(8)> q = Fifo.in!(3, q)
{[3], []}
iex(9)> q = Fifo.in!(2, q)
{[2], [3]}
iex(10)> q = Fifo.in!("r", q)
{["r", 2], [3]}
iex(11)> q
{["r", 2], [3]}

Also bear in mind that erlang usually has the data in the last argument(common in many other functional languages, it is useful when using currying and partial function application), but in elixir it’s more common to have the data(in this case the queue) in the first argument, so you can leverage the pipe |> operator:

defmodule Fifo do
  def new do
    :queue.new()
  end

  def in!(q, x) do
   :queue.in(x, q)
  end

  def out!(q) do
    :queue.out(q)
  end
end

q =
  Fifo.new()
  |> Fifo.in!(3)
  |> Fifo.in!(2)
  |> Fifo.in!("r")
#=> {["r", 2], [3]}