IMO, I dislike this quote it is quite misleading if you know who is your enemy then reaching out a hand in friendship will just get you bitten. But you can't know who is your enemy beforehand so you should reach out a hand in friendship to everyone because your prejudices are often incorrect and you will find a friend where you thought there was an enemy.
Failing to reach out a hand in friendship will make them the enemy which is very difficult to reverse; whereas if you reach out a hand in friendship and find an enemy you can always retract the hand.
I extend my hand in friendship - if you want to accept that hand I will be loyal and non judgemental, If you don't accept-there are other people who will. I don't want or need enemies but a few more can be added to the list if necessary. I prefer friendship.