> **CAVEAT** 
> The solution below does not check for incomplete / malformed command invocation! For example, if `--p_out` requires an argument, but the command is called as `my-script.sh --p_out --arg_1 27` then it will happily assign the string `"--arg_1"` to the `p_out` variable.

This answer was initially an edit of [@cdmo's answer][1] (thanks to @Milkncookiez's comment also!), that got rejected as expected.

When using the variables, one can make sure that they have a default value set by using `"${p_out:-"default value"}"` for example.

From [3.5.3 Shell Parameter Expansion][2] of the GNU Bash manual:

> **`${parameter:-word}`** 
> If parameter is unset or null, the expansion of word is substituted. Otherwise, the value of parameter is substituted.

 #!/usr/bin/env bash
 
 while [ $# -gt 0 ]; do
 case "$1" in
 -p|-p_out|--p_out)
 p_out="$2"
 ;;
 -a|-arg_1|--arg_1)
 arg_1="$2"
 ;;
 *)
 printf "***************************\n"
 printf "* Error: Invalid argument.*\n"
 printf "***************************\n"
 exit 1
 esac
 shift
 shift
 done
 
 # Example of using the saved command line arguments.
 # WARNING: Any of these may be an empty string, if the corresponding
 # option was not supplied on the command line!

 echo "Without default values:"
 echo "p_out: ${p_out}"
 echo "arg_1: ${arg_1}"; echo

 # Example of using parsed command line arguments with DEFAULT VALUES.
 # (E.g., to avoid later commands being blown up by "empty" variables.)

 echo "With default values:"
 echo "p_out: ${p_out:-\"27\"}"
 echo "arg_1: ${arg_1:-\"smarties cereal\"}"

If the above script is saved into `my-script.sh`, then these invocations are all equivalent:

 $ . my-script.sh -a "lofa" -p "miez"
 $ . my-script.sh -arg_1 "lofa" --p_out "miez"
 $ . my-script.sh --arg_1 "lofa" -p "miez"

(where `.` is Bash's [`source`][3] command.)

To demonstrate the default values part, here's the output without any arguments given:

 $ . my-script.sh
 Without default values:
 p_out:
 arg_1:
 
 With default values:
 p_out: "27"
 arg_1: "smarties cereal" 


 [1]: https://unix.stackexchange.com/a/204927/85131
 [2]: https://www.gnu.org/savannah-checkouts/gnu/bash/manual/bash.html#index-parameter-expansion
 [3]: https://ss64.com/bash/source.html