How to delete an exact element in a bash array?

Use the unset command with the array value at index, something like this:

#!/usr/bin/env bash
ARRAY=(foo bar any red alpha number of keywords rd3.0 and)
keywords=(red, rednet, rd3.0)

index=0
for keyword in ${ARRAY[@]}; do
      if [ "$keyword" = "red" ] || [ "$keyword" = "rd3.0" ] || [ "$keyword" = "rednet" ]; then
           # HERE IS TROUBLE
           # ARRAY=( ${ARRAY[@]/"$p"/} )
           unset ARRAY[$index]
           echo "ARRAY is now: ${ARRAY[@]}"
           break
      fi
      let index++
 done