the problem is you're trying to use regex features not supported by grep. namely, your \d
won't work. use this instead:
REGEX_DATE="^[[:digit:]]{2}[-/][[:digit:]]{2}[-/][[:digit:]]{4}$"
echo "$1" | grep -qE "${REGEX_DATE}"
echo $?
you need the -E
flag to get ERE in order to use {#}
style.