It is a little bit hard to know how environmental concerns will affect the globalizing economy. There are at least three possibilities.
On the one hand, concern about the environment might make the economy more globalized. As countries become more concerned about the economy, they might make more rules to reduce the environmental impact of the world economy. This would increase globalization because it would impose one set of rules on all countries.
On the other hand, it is possible that concerns about the environment will cause there to be less globalization. It is very possible to imagine the countries of the world being unable to agree on how to handle environmental concerns. Developing countries might want to pursue economic growth even if it harms the environment. Countries that are already rich might want more rules to protect the environment. As the two sets of countries quarrel over their different desires, they might stop cooperating with one another. They might make different sets of rules, thus breaking up the global economy.
A third possibility is that environmental concerns will slow the global economy. Rules might be imposed which make it harder for economic activity to occur. This would reduce the rate of growth in the global economy.
It is not possible to know which of these effects will actually come about, or if environmental concerns will affect the globalized economy in some other way.