Shell – How to check for “delta” argument like “+10”

Your requirements are logically contradictory. Given input like gitploy up -t 2.0.0 test_repo, you need to parse the options, and in particular notice the presence of the -t option and the fact that it takes one argument, in order to identify that the first non-option argument is test_repo.

So first parse the options normally. Then you can know what the first operand is. At that point, process the options. Store the information you need about the options in variables.

action="$1"
shift
unset t_arg
while getopts "zhvdurqw:c:i:e:o:b:t:f:p:g" opt; do
  case "$opt" in
    c) c_arg="$OPTARG";;
    …
  esac
done
shift "$((OPTIND-1))"
root_arg="$1"

if [ -n "${c_arg+1}" ]; then
  queue_callback "$OPTARG"
  echo "$root_arg was here"
fi

I'd try to use bash variable substitution:

   test)
        shift
        docker exec -it $(docker-compose ps -q web) python manage.py test "${@-apps}"
        ;;

Other way is to check $* instead of $1:

case $* in 
    bash)
         ...
    test)
         docker exec -it $(docker-compose ps -q web) python manage.py test apps
         ;;
    test\ *)
         docker exec -it $(docker-compose ps -q web) python manage.py test "${@:2}"
         ;;