Here's a quick and dirty way to opt out for BASH and ZSH users for easy copy/pasting.

BASH:

  cat <<EOF >> .bashrc
  # Opt out of Homebrew analytics
  export HOMEBREW_NO_ANALYTICS=1
  if [[ -e "$HOME/.homebrew_analytics_user_uuid" ]]; then
    rm -f "$HOME/.homebrew_analytics_user_uuid"
  fi
  EOF

ZSH:

  cat <<EOF >> .zshrc
  # Opt out of Homebrew analytics
  export HOMEBREW_NO_ANALYTICS=1
  if [[ -e "$HOME/.homebrew_analytics_user_uuid" ]]; then
    rm -f "$HOME/.homebrew_analytics_user_uuid"
  fi
  EOF

Cheers.