This is an interesting question and one that at least need to be considered in the light of three things 1) God's actions, 2) God's actions in light of sin, and 3) the implications for man.
When we think about God, we do understand that God indeed does take care of his creation. It is his earth: "The earth is the Lord's and the fullness thereof" (Psalm 24:1). We are told to "Consider the birds of the air: they neither sow nor reap nor gather into barns, and yet Your heavenly father feeds them... the lilies of the field, how they grow; they neither toil nor spin, yet even Solomon in all his glory was not arrayed as one of these." (Matthew 6: 26, 28b-29) God himself takes care of all things. God takes care of and preserves all his creatures and his land. We understand that all first article (of the creed) gifts come from and are preserved by God.
Yet, think on sin and its consequences. Did not God, who takes care of all things, destroy the earth in the flood? It's a harsh reminder that the world we live in is fallen and after the fall, sin had to be dealt with. God's plan of salvation had always been one of sending a redeemer to reconcile all the earth to himself. "For the creation was subjected to futility, not willingly, but because of him who subjected it, in hope that the creation itself will be set free from its bondage to decay and obtain the freedom of the glory of the children of God." (Romans 8:20-21) And truly the earth will be created anew in perfection on the last day. But until then we live in a fallen world. We live in a world that is falling into chaos, not merely because of what man does in polluting the environment, but also because it too is a fallen creation.
But, finally, how does this effect man. Man as we know was commanded by God in the garden to "be fruitful and multiply and fill the earth and subdue it and have dominion over... every living thing that moves on the earth." (Genesis 1:28) We also know that man was created as the capstone of creation. No other creature was made in the image of God, nor was the command to subdue creation and have dominion given to any other. We are the stewards of God's earth. We are not equal with the other creatures, nor are we even subservient to them. We are the overseers of creation working and tending as commanded by God.
So the real question in all of this - concerning how God acts, the state of the world and the role of overseer that God as given us as human beings, is failing to be "green" (defined in the best sense) a sin?
As I understand it - yes. Failing to be a good steward of God's gifts is a sin. And one can follow the rabbit hole all the way down, and it will drive a man to despair that he is such a dreadful sinner deserving of hell since he cannot be perfectly "green".
But why stop there? If you look at any aspect of life, you will find the same thing - an endless trail of things to do that God desires of you, lest you sin. Yet, it seems that because it is not on the forefront of the public display, you can easily fool the mind and heart into believing it has fulfilled God's law, when it has not.
But, thus is the fallen world. There is sin there. There will always be more and more ways to do the will of the Father. And, it is too much for a sinner. He has not the strength to do it all himself. That is why Christ came, and forgave man by his blood. All this that you might live in the freedom of the Gospel not bound by the law but free to do the good works with a free conscience. That you might not be paralyzed by the greatness of your sin, but free to serve God and your neighbor... even by being "green". :)