Matthew 5:13-16 is for the Israelites ONLY? We are having a discussion about how we, as a follower of Christ, are the ‘salt of earth and light of the world’ (Matthew 5:13-16).  

Someone insists that the verses are for the Israelite people/disciples only and it is not applicable for us Gentiles/believers now.  

We tried to explain and give them verses like 2 Timothy 3:16-17, Galatians 3:28, etc.
They also insists that certain parts of the Scripture are for the Israelites people only, this even includes the Great Commission and other teachings of Jesus.   

Can you help me explain better to them the opposite position: that Matthew 5:13-16 is not for the Israelites only.
You are encountering a theology called Dispensationalism.

Plenty of sites will give you an overview, and many better than Wikipedia, but a key part of their theology is that God dealt with Man in distinct ways in distinct times. Most hold that the change from the 'Old Covenant' to the 'New Covenant' occurred only after the death of Jesus (usually at Acts 2) and that until then all teaching - including the teaching of Jesus - was under the Old Covenant. The Old Covenant was superceded by the New, and its teaching made irrelevant.This irrelevant teaching includes the teaching of Jesus.

I'm not going to get into the rights and wrongs. Dispensationalism is widespread in the United States, and results in significant numbers of people who call themselves Christian yet believe that the teachings of their God in the person of Jesus are irrelevant to them, and indeed were irrelevant only a few years (or even hours) after they were taught. It's easy to work out the implications of that in the current climate.

I'm afraid I'm going to have to leave finding Biblical arguments against this position for yourself, but you might start asking them for the Biblical support of their claims. If you are part of a church that does not hold dispensationalist beliefs, talk to your church leaders about this theology and the church's attitude to it.