I feel your first example is better written like this:

    if ! ansible-playbook ... ; then 
        echo -e "\e[1;31m""Error when executing ansible!""\e[0m"
        exit 1
    fi

But generally when I need to work around errexit, I tend to add something like " || true" or " || xyz_failed=true" to the end of the command line instead of turning it off and on again.