There's a tension in faith. It's complicated, really. The tension is that we receive everlasting life by placing our faith in Christ's atoning death on the cross (John 3:16), but the way we live reflects whether or not we've placed our faith in Christ. The way we live doesn't change whether or not we receive the everlasting life – it's just a reflection and a result of belief and faith. That's complicated, and it's a tension that Christians live with. The problem for Israel as Amos wrote the prophecy is that the people didn't live any differently than the surrounding nations. Again, holy living wasn't then nor is it now a means to salvation. However, holy living reflects a life that is surrendered to the Lord. The lack of holy living showed that the people weren't really trusting the Lord; they were living as the other nations lived: using God as a god to be manipulated so they might get what they desired.
How is the tension in your life? Are you living in a way that reflects a surrender to the Lord if you have, in fact, decided to trust Him? Those who trust the Lord have lives that reflect such a trust. It's not as a means of earning salvation but as a response of gratefulness to a God who has given so much.