I don't see any similarity between the Golden Rule and an eye for an eye. That's difference between the positive and the negative formulations of the Golden Rule.
An eye for an eye speaks to me more about seeking revenge than with trying to get along and loving your neighbor.
When God gave the command of eye for eye, strike for strike, and life for life to His Covenant people these had nothing to do with revenge.
Nothing at all.
Do you even know the original command God gave to His Covenant people on who they were instructed to love and who is the identity of "neighbor" is?
By your comment you think "neighbor" means the guy or gal that lives next door to you in your apartment complex who is unsaved. God never commanded His people to love the unsaved. As a matter of fact, it'd be hypocritical for God to command His people "do not love the world (unsaved people) nor the things in the world. If any man loves the unsaved (world) the love of the Father is not in them., and then to turn around and He Himself love the world which is the error in the Church that God's loves everyone and Christ died for everyone.
I believe we're called to love unsaved people into the kingdom of God. The way to do that is tell them about Jesus and what he has done for them on the Cross. John 3:16
Well, that's your belief but it's not biblical nor did God ever instruct, guide, command, nor even hint that His Covenant people love non-covenant people.
Paul and Barnabas were called out by the Holy Spirit and given a commission to do a thing for God in Acts 13. By your saying that "you tell people about Jesus" mean God has specifically given you a calling to do that and gifted you with spiritual gifts to accomplish that call like He did Paul and Barnabus? Because Paul described the body of Christ in 1 Corinthians 12-14 and Romans 12 like a body with many members and each part of the body functioning in that thing for which it was given function to do. What place/part in the body of Christ are you and what are your spiritual gifts to accomplish that call? Do you even know? Because if God hasn't spoken directly to you and revealed your place in the body of Christ and your gifts and you just UP and do what you want, you're not an obedient servant/Christian. You're like a ship without a rudder and a horse without a bit in your mouth. Being tossed in the waves and maverick.
You see, if and when God is going to use someone in the body of Christ, He calls them and reveals their place in the body and their function and also instruction in what to do and what to say and when to do it and when to say it. And He equips His servants. The model and teaching is in Scripture. Study it. If you want to be used of God study His Word, stay in prayer, ask Him, and when His time is right, He'll speak to you. But not before. God uses obedience not disobedience, and if you're out there in the world telling people about Jesus and they haven't even asked you you're not doing God service. To obey is better than sacrifice for disobedience is as witchcraft. God doesn't use rebellion. So, think about it. Until God speaks to you live your life as peaceably as much as possible with all men and learn to do your own business and always be ready to give an answer to those that ask of the hope in you with meekness and fear. And if they're not asking then say nothing. You're supposed to be a living epistle to be read of all men. But if you're out there pushing Jesus on people that haven't asked of the hope in you then all you're doing is pushing them away because nobody wants to hear about God and Jesus Christ. They have one master and really resent it when you try to push another Master on them, and they hate your Master. God can't and doesn't use this.
The bottom line is to do to other people everything, without exception, that love and Jesus’ commandments require.
You do know that God's Word is holy, right?
So, if God is not giving that which is holy to dogs why are you?
You do know the Word of God is symbolized as Pearl, right?
So, if God is not casting His pearls to swine why are you?
Unless of course, God has placed you in the body of Christ and has revealed your place to you and given you certain spiritual gifts to accomplish that function for Him. If God hasn't done this then you're copying and mimicking other Christian's place in the body and their function and pretty much just making things worse. In the Kingdom of God the King has Court and not everyone in His Court has the same function. The royal cook doesn't just go over to the motor-pool, take the keys off the rack, and take the King's buggy out for a spin. There would be consequences to pay.
The eye functions as the eye because that's how God created the eye to function. It'd be a deformed body if the eye didn't know it was an eye and started acting like an ear or a foot. You understanding this? Well, it's biblical. God teaches it in His Word. Study it. And wait on the Lord. Be obedient and wait on the Lord.