This is mostly a straw man argument. It's always a mistake to represent diverse groups like "environmentalists" as holding a homogeneous belief. There are certainly some environmentalists who believe what you just said, but as an environmentalist, I don't believe that, and I think the environmentalists who do believe that are the minority of environmentalists.
On the contrary, for me, environmentalism isn't about saving the planet, it's about saving humans. The planet doesn't need saving: if we turn the planet into a barren wasteland it will uncaringly continue hurtling through space without us, but we'll be dead. The environment is a necessary component to human survival and thriving. I don't believe that means we should have no impact on the environment--that's not possible--but that we need to be careful about when we change our impact on the environment, because we risk breaking the fragile ecosystems that have supported our existence.
No. At best that's a position held only by a tiny and extreme minority.
Consider "Permaculture", a school of applied ecology that's become popular all over the world since it was started by a government-employed ecologist and co. in the late 1970's. The explicit goal of this design school is to create and maintain agriculturally productive ecosystems that improve soil fertility and volume over time (the "permanent" part of "Permanent Agriculture".)
With applied ecology we could probably increase the carrying capacity of the Earth to the point of having, say, 20B people while also increasing biodiversity and climate and long-term stability and all that good stuff.
IMO this particular aspect of modern environmentalism is a religious root on a secular tree.
Many religions imply that man isn't natural, that there's the nature world and that we are above it/not part of it. That core belief carries over into secular society/people even though they no longer believe the system of thought that lead to that conclusion.
I assert that man is in fact natural not supernatural, and that the changes man makes to the world as as natural of a process a trees overgrowing a grassland to make a forest or an ocean eroding away an island.
There's other fallacious ideas around nature that may have nothing to do with religion that I think are just common breakdowns in logic. People commonly apply the idea of "balance" to areas where it doesn't apply, or at least doesn't apply in the way that they think it does. Earth is a complicated system of systems, but is it meant to be in balance? If that were so, Earth's climate would not oscillate (excluding changes in solar output) over geological eras. Was Earth out of balance during the ice age?
"Balance" may in part be a proxy for our desire to want systems with which we are accustomed to not change. I've witnessed countless individuals, concerned with preserving nature, who would consider a plant or animal to be "non-native" or "invasive" while failing to recognize that the plants they believe to be "native" were introduced by animals in recent ecological history. They overlook the possibility (really a high likelihood) that the environment that explorers set foot on was significantly different from how it was even a century prior. It'd difficult for concepts of nativeness and invasiveness to be comprehensible if they did. Not that these aren't useful concepts in some domain, but many people interested in ecology or environmentalism believe them to be absolutely accurate or meaningful.
So continual world war seems the only way to become sustainable.
Even that is a bit difficult. We're really talking about reducing the carrying capacity of the earth in most scenarios for both humans and other animals. Environmentalism is saying that many humans will die on the default path, and this is a path that can be diverted with sufficient action. The longer we wait, the worse the action is going to need to be and the more people that may die.
But nuances are difficult to communicate when the other side is working in wholesale disinformation.