I would not use sed instead use egrep -i -v (-i case insensitive -v does not match pattern):
egrep -i -v "$(echo ${ARRAY1[@]} | tr ' ' '|')" /etc/file
the expression
echo ${ARRAY1[@]}
because it has no quotes will not print new line making a space delimited string with all the strings in the array.
tr ' ' '|'
will replace all spaces with \| (or) for the grep expression which will build the pattern for your grep command.
Now if you insist on using sed there are a couple of options one of which would look something like:
sed -i $(echo ${ARRAY1[@]} | sed -e 's:\w\+:-e "/\1/d":g') /etc/file
This will create a separate -e "/stringFromArray/d" for the sed base sed command
NOTE: make sure that there are no spaces or "/$|" in the strings in your array. If there are depending on what solution you try it could get in the way.