Parse Bash arguments without getopts or getopt

args_parser.sh

#!/bin/bash
# Dennis Ullrich
# Version 0.1-0 (2017-06-29)
# request@decstasy.de

# Bash Version 3 required (it also works with ksh)
[[ ${BASH_VERSINFO[0]} -lt 3 ]] && exit 1

# Defaults
stdin=0
csv=0
param=""

# Put all arguments in a new array (because BASH_ARGV is read only)
ARGS=( "$@" )

for i in "${!ARGS[@]}"; do
        case "${ARGS[i]}" in
                '')             # Skip if element is empty (happens when it's unsetted before)
                                continue
                        ;;
                -s|--stdin)     stdin=1
                        ;;
                --csv)          csv=1
                        ;;
                -p|--param)     # Use +1 to access next array element and unset it
                                param="${ARGS[i+1]}"
                                unset 'ARGS[i+1]'
                        ;;
                --)             # End of arguments
                                unset 'ARGS[i]'
                                break
                        ;;
                *)              # Skip unset if our argument has not been matched
                                continue
                        ;;
        esac
        unset 'ARGS[i]'
done

# In case you want to process more, there is nothing lost except the already parsed arguments with options.
# Keep in mind there was not a single shift!
echo "Unused Arguments:"
for i in "${!ARGS[@]}"; do
        echo "$i: ${ARGS[i]}"
done

Nice work but I see one problem which are empty parameters. You simply ignore them because of the first case.
Example

--arg1 --arg2 '' --arg3 -- blah

both options are without value so expected parsing would be

--arg1 --arg2 --arg3 -- '' blah

There must be implemented other way of skipping args. Simply using a skip flag could help, like

skip=''
for i in "${!ARGS[@]}"; do
        [[ -n "$skip" ]] && {
                skip=''
                continue
        }
        case "${ARGS[i]}" in
                -p|--param)     # Use +1 to access next array element and unset it
                                param="${ARGS[i+1]}"
                                unset 'ARGS[i+1]'
                                skip=1
                        ;;

or use other way of iteration:

for (( i=0; i<${#ARGS[@]}; i++ )); do
        case "${ARGS[i]}" in
                -p|--param)     # Use +1 to access next array element and unset it
                                param="${ARGS[i+1]}"
                                unset 'ARGS[i]'
                                let i++
                        ;;

Also your implementation does not allow short version of short options -abc as -a -b -c
This pre-processing should help

  local ARGS=()
  for i in "$@"; do
    if [[ "${i:0:1}" == "-" && "${i:1:1}" != "-" ]]; then
      for (( j=1; j<${#i}; j++ )); do
        ARGS+=("-${i:$j:1}")
      done
    else
      ARGS+=("$i")
    fi
  done

It is not almighty, though.